Infobox scientist name HeisukeHironaka image image width birth date birth date and age 1931 04 09 df y birth place death date death place nationality flag JPN name Japanese field Mathematics work institutions Harvard University br Columbia University br Seoul National University alma mater Harvard University doctoral advisor Oscar Zariski doctoral students William Haboush br Allen Tannenbaum br Bernard Teissier known for prizes Fields Medal 1970 HeisukeHironakaHironakaHeisuke born 9 April ... by HeisukeHironaka and Hideyuki Matsumura 1967 On the characters math nu math and math tau math of singularities by HeisukeHironaka Introduction to the theory of infinitely near singular points HeisukeHironaka 1974 The theory of the maximal contact Jos M. Aroca, HeisukeHironaka and Jos L. Vicente 1975 Desingularization theorems Jose M. Aroca, HeisukeHironaka and Jose L. Vicente 1977 Geometric singularity theory editors of the volume, HeisukeHironaka, Stanis aw Janeczko 2004 References Reflist External links MathGenealogy id 18752 MacTutor Biography id Hironaka Jackson, Allyn http www.ams.org notices 200509 fea hironaka.pdf Interview with HeisukeHironaka Notices of the American Mathematical ... Persondata . NAME Hironaka, Heisuke ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1931 04 09 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Hironaka, Heisuke Category 1931 births Category ... asia mathematician stub japan scientist stub zh min nan HironakaHeisuke da HeisukeHironaka de HeisukeHironaka es HeisukeHironaka fr HeisukeHironaka ko it HeisukeHironaka nl HeisukeHironaka ja pnb pt HeisukeHironaka ru , sk HeisukeHironaka fi HeisukeHironaka uk vi HironakaHeisuke zh ... equivalence birationally equivalent to a similar variety which has no singularities. Hironaka ... as Issa s theorem in complex function theory. Hironaka is married to Wakako Hironaka , a politician ... more details
Infobox Planet minorplanet yes width 25em bgcolour FFFFC0 apsis name Hironaka symbol image caption discovery yes discovery ref discoverer K. Endate and K. Watanabe discovery site Kitami discovered September 12, 1993 designations yes mp name 6978 alt names 1993 RD named after HeisukeHironaka mp category orbit ref epoch May 14, 2008 aphelion 3.0050555 perihelion 2.1217521 semimajor eccentricity 0.1722911 period 1499.0771306 avg speed inclination 7.47159 asc node 339.26202 mean anomaly 264.07342 arg peri 302.02261 satellites physical characteristics yes dimensions mass density surface grav escape velocity sidereal day axial tilt pole ecliptic lat pole ecliptic lon albedo temperatures temp name1 mean temp 1 max temp 1 temp name2 max temp 2 spectral type abs magnitude 13.1 6978 Hironaka 1993 RD is a Asteroid belt main belt asteroid discovered on September 12, 1993 by K. Endate and K. Watanabe at Kitami . External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 6978 Hironaka JPL Small Body Database Browser on 6978 Hironaka MinorPlanets Navigator 6977 Jaucourt 6979 Shigefumi MinorPlanets Footer DEFAULTSORT Hironaka Category Main Belt asteroids Category Asteroids named for people Category Discoveries by Kazuro Watanabe Category Discoveries by Kin Endate Category Astronomical objects discovered in 1993 beltasteroid stub fa it 6978 Hironaka hu 6978 Hironaka ja pl 6978 Hironaka pt 6978 Hironaka ... more details
japanese name T d T d Heisuke 1844 December 13, 1867 was a samurai of Japan s late Edo period who served as the eighth unit captain of the Shinsengumi . His full name was T d Heisuke Fujiwara no Yoshitora . Background T d was from Edo, Musashi Province now Tokyo . Very little is known about his origin. Although he was said to be an illegitimate child of T d Takayuki , the 11th generation lord of the Tsu domain , this is highly debatable. However, one argument some use in favor of this theory is the fact that he possessed a sword made by Kazusa no suke Kaneshige, who was a swordmaker under the patronage of the Tsu domain and that such a sword would be difficult for a mere r nin to obtain, even by heritage. Another point that suggests possible Tsu domain heritage is his formal given name imina , Yoshitora , which shares a character in common with the name of the first T d lord of Tsu, T d Takatora . T d was a practitioner of the Hokushin Itt ryu , trained at Chiba Shusaku Narimasa s dojo. However, according to some sources, he was trained at It Kashitar s dojo instead. In around 1862, he started taking his meals at Kondou Isami s Shieikan. Shinsengumi Period In 1863, T d joined the Roshigumi with Kond and other members of the Shieikan. After the Shinsengumi was formed, T d first became a fukuch jokin assistant vice commander and then became the captain of the eighth unit in 1865. ref Yamamura, Tatsuya. Shinsengumi Kenkyaku Den . Tokyo PHP Kenky jo, 1998, p.186 ref Sources vary as to his role in the Serizawa Kamo one of the original commanders of the Shinsengumi assassination. T d received a wound on his forehead during the Ikedaya Jiken on July ... 4569601766 Persondata Metadata see Wikipedia Persondata . NAME Todo, Heisuke ALTERNATIVE NAMES ..., Heisuke Category Samurai Category Shinsengumi Category 1844 births Category 1867 deaths Category Japanese swordsmen de T d Heisuke es T d Heisuke ko ja vi T d Heisuke zh ... more details
Infobox Military Person name Heisuke Yanagawa lived October 2, 1879 Death date and age 1945 01 22 1879 10 02 placeofbirth Nagasaki prefecture , Japan placeofdeath image image Yanagawa Heisuke.jpg 180px caption General Heisuke Yanagawa nickname allegiance Empire of Japan branch Image War flag of the Imperial Japanese Army.svg 22x20px border Imperial Japanese Army serviceyears 1900 1945 rank Lieutenant General commands IJA 1st Division, Taiwan Army, IJA 10th Army unit battles Russo Japanese War br Second Sino Japanese War br World War II awards family party Taisei Yokusankai laterwork Ministry of Justice Japan Minister of Justice Japanese name Yanagawa nihongo Heisuke Yanagawa Yanagawa Heisuke extra 2 October 1879 22 January 1945 was a general in the Imperial Japanese Army in World War II . Biography Born in what is now part of Nagasaki, Nagasaki Nagasaki city , Nagasaki prefecture , Yanagawa was raised in ita Prefecture by his adoptive parents. He graduated from the 12th class of the Imperial Japanese Army Academy in 1900, and served in combat during the Russo Japanese War of 1904 1905. He graduated from the 24th class of the Army War College Japan Army Staff College in 1912. After serving as an instructor in the Army Cavalry School, he was appointed a military attach to China and served as an instructor at the Beijing Army College in 1918. He later traveled to Europe as part of Japan s delegation to the Versailles Peace Treaty negotiations, and from 1920 1923 was a member ... first Steen url http www.generals.dk general Yanagawa Heisuke Japan.html title Yanagawa Heisuke ... Metadata see Wikipedia Persondata . NAME Yanagawa, Heisuke ALTERNATIVE NAMES SHORT DESCRIPTION ... OF DEATH DEFAULTSORT Yanagawa, Heisuke Category 1884 births Category 1973 deaths Category People ... of Japan Category Nanking Massacre ko id Heisuke Yanagawa ja ru , vi Yanagawa Heisuke zh ... more details
nihongo Wakako HironakaHironaka Wakako extra born 11 May 1934, Tokyo is a Japanese writer and politician. She is a member of the House of Councillors Upper House of the Japanese Diet . Her political affiliation is with the Democratic Party of Japan . Her husband is HeisukeHironaka , a mathematician . Politician Wakako Hironaka has been a member of the House of Councillors since 1986, and currently serving her fourth term. Between 1993 1994, she was State Minister, Director General of the Environment Agency in the Hosokawa Cabinet. In the past years, she served several times as Vice President of the Democratic Party of Japan. Councillor Hironaka is currently Director of the Research Committee on International Affairs and Global Warming Issues and a Member of both the Committee on Environment and Official Development Assistance and Related Matters. She has been active internationally, as Vice Chair of Global Environmental Action GEA , an organizing member of Micro Credit Summit, a member of World Commission on Forests and Sustainable Development, Earth Charter Commission, and Teri The Energy and Resource Institute Ms. Hironaka received a B.A. in English from Ochanomizu University Ochanomizu Women s University and an M.A. in Anthropology from Brandeis University . She has written several books, essays, translations, and critiques on education, culture, society, and women s issues. Other activities Party Affiliation and Position Standing Officer, Democratic Party of Japan Membership, House Committees Chair, Research Committee on Economy, Industry and Employment Member, Committee on Education, Culture, and Science. Membership, International Organizations Vice Chair, Global ... . NAME Hironaka, Wakako ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Hironaka, Wakako Category Government ministers of Japan Category Members ... Japan politician 1930s stub de Wakako Hironaka es Wakako Hironaka fr Wakako Hironaka ja ... more details
Infobox martial artist name Kuniyoshi Hironaka other names image image size 200px alt caption birth name birth date birth date and age 1976 06 17 birth place Yamaguchi, Yamaguchi Yamaguchi , Japan death date death place death cause residence nationality flagicon Japan Japanese people Japanese height height ft 5 in 10 weight convert 155 lb kg st abbr on weight class Lightweight MMA Lightweight br Welterweight MMA Welterweight reach style Brazilian Jiu Jitsu , Judo stance fighting out of team Academia Az rank years active mma win 16 mma kowin 6 mma subwin 5 mma decwin mma loss 8 mma koloss mma subloss mma decloss mma draw mma nc url sherdog footnotes updated nihongo Kuniyoshi HironakaHironaka Kuniyoshi extra born June 17, 1976 is a Japanese people Japanese mixed martial artist who competes in the Welterweight MMA welterweight division. After Mizuto Hirota vacated the Cage Force Lightweight Championship, Kuniyoshi Hironaka defeated Yoshihiro Koyama at Cage Force Cage Force 12 to become the new belt holder. TOC Mixed martial arts record ALL THE HIDDEN SPANS ARE FOR PROPER TABLE SORTING. PLEASE DO NOT EDIT THEM UNLESS YOU KNOW WHAT YOU RE DOING. MMArecordbox wins 16 losses 8 ko wins 6 ko losses 5 sub wins 5 sub losses 1 dec wins 5 dec losses 2 style font size 85 text align left class wikitable sortable width 99 style border style none none solid solid background e3e3e3 Result style border style none none solid solid background e3e3e3 Record style border style none none solid solid background e3e3e3 Opponent style border style none none solid solid background e3e3e3 Method style border style none none solid solid background e3e3e3 Event style border style none none solid solid background e3e3e3 Date style border style none none solid solid background e3e3e3 Round style border ... see Wikipedia Persondata . NAME Hironaka, Kuniyoshi ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH ... DEFAULTSORT Hironaka, Kuniyoshi Category Living people Category 1976 births Category Japanese mixed ... more details
Infobox scientist name Bernard Teissier image filename only image size caption birth date birth place death date death place nationality flag FRA name French fields Mathematics workplaces Paris Diderot University br Paris Sud 11 University br University of Tehran alma mater Paris Diderot University doctoral advisor Heisuke Hironaka doctoral students Pedro Gonz lez P rez br Herwig Hauser br Fran ois Loeser known for awards Bernard Teissier is a France French mathematician and a member of the Nicolas Bourbaki group. His research interests include commutative algebra and algebraic geometry . Teissier attained his doctorate from Paris Diderot University in 1973, under supervision of Heisuke Hironaka . External links MathGenealogy id 13781 http people.math.jussieu.fr teissier Website Persondata Metadata see Wikipedia Persondata . NAME Teissier, Bernard ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Teissier, Bernard Category Year of birth missing living people Category Living people Category French mathematicians Category 20th century mathematicians Category 21st century mathematicians Category University of Paris alumni France mathematician stub de Bernard Teissier ... more details
The Research Institute for Mathematical Sciences RIMS is attached to Kyoto University in Japan . RIMS is a research institute of the only mathematics in Japan founded in 1963 . Notable mathematicians Heisuke Hironaka , Fields Medalist Shigefumi Mori , Fields Medalist Kiyoshi It , Wolf Prize in Mathematics laureate External links http www.kurims.kyoto u.ac.jp home page coord missing Japan Category Mathematical institutes Category Kyoto University Category Research institutes in Japan kyoto university stub de Research Institute for Mathematical Sciences ko ja ... more details
In mathematics , in particular in algebraic geometry , a complete algebraic variety is an algebraic variety X , such that for any variety Y the Product category theory projection Regular map algebraic geometry morphism nowrap X Y Y is a closed map , i.e. maps closed set s onto closed sets. ref Here the product category theory product variety X Y does not carry the product topology , in general the Zariski topology on it will have more closed sets except in very simple cases . ref The most common example of a complete variety is a projective variety , but there do exist complete and non projective varieties in Dimension of an algebraic variety dimensions 2 and higher. The first examples of non projective complete varieties were given by Masayoshi Nagata ref Existence theorems for nonprojective complete algebraic varieties, Illinois J. Math. 2 1958 490 498. ref and Heisuke Hironaka . citation needed date August 2010 An affine space of positive dimension is not complete. The morphism taking a complete variety to a point is a proper morphism , in the sense of scheme theory . An intuitive justification of complete , in the sense of no missing points , can be given on the basis of the valuative criterion of properness , which goes back to Claude Chevalley . Notes reflist References Section II.4 of Hartshorne AG Chapter 7 of Citation last Milne first James S. title Algebraic geometry year 2009 version v. 5.20 url http jmilne.org math CourseNotes ag.html accessdate 2010 08 04 Section I.9 of Citation last Mumford first David author link David Mumford title The red book of varieties and schemes year 1999 publisher Springer Verlag edition Second, expanded doi 10.1007 b62130 series Lecture notes in mathematics volume 1358 isbn 978 3 540 63293 1 DEFAULTSORT Complete Algebraic Variety Category Algebraic varieties sv Komplett varietet ... more details
saved book title The Fields Medal subtitle And its recipients cover image FieldsMedalFrontArchimedes.jpg cover color DarkRed The Fields Medal And its recipients Overview Fields Medal International Mathematical Union International Congress of Mathematicians John Charles Fields R. Tait McKenzie 1936 Lars Ahlfors Jesse Douglas 1950 Laurent Schwartz Atle Selberg 1954 Kunihiko Kodaira Jean Pierre Serre 1958 Klaus Roth Ren Thom 1962 Lars H rmander John Milnor 1966 Michael Atiyah Paul Cohen mathematician Paul Cohen Alexander Grothendieck Stephen Smale 1970 Alan Baker mathematician Alan Baker Heisuke Hironaka Sergei Novikov mathematician Sergei Novikov John G. Thompson 1974 Enrico Bombieri David Mumford 1978 Pierre Deligne Charles Fefferman Grigory Margulis Daniel Quillen 1982 Alain Connes William Thurston Shing Tung Yau 1986 Simon Donaldson Gerd Faltings Michael Freedman 1990 Vladimir Drinfel d Vaughan Jones Shigefumi Mori Edward Witten 1994 Jean Bourgain Pierre Louis Lions Jean Christophe Yoccoz Efim Zelmanov 1998 Richard Borcherds Timothy Gowers Maxim Kontsevich Curtis T. McMullen 2002 Laurent Lafforgue Vladimir Voevodsky 2006 Andrei Okounkov Grigori Perelman Terence Tao Wendelin Werner 2010 Elon Lindenstrauss Ng B o Ch u Stanislav Smirnov C dric Villani Category Wikipedia books on award winners ... more details
100894 HeisukeHironaka , http books.google.com books?hl en&lr &id q6eSjV 0egUC&oi fnd&pg PA487&dq On the Work of Shigefumi Mori Heisuke Hironaka&ots rhUYrej Gw&sig xwoIIXKbawqBUy6BprFpoDkogLQ v onepage&q ... more details
Year nav topic 1970 science The year 1970 in science and technology involved some significant events, listed below. Astronomy and space exploration February 11 Japan becomes the fourth country to launch a satellite into orbit. March 31 Explorer I reentry after 12 years in orbit April 11 Apollo 13 ill fated space mission launched April 17 Apollo 13 returns safely to earth August 17 Venera program Venera 7 is launched. It will later becomes the first spacecraft to successfully transmit data from another planet . November 17 Luna program The Soviet Union lands Lunokhod 1 on Mare Imbrium Sea of Rains on the Moon . This is the first roving remote controlled robot to land on another world and was released by the orbiting Luna 17 spacecraft. Computer science January 1 Unix epoch at 00 00 00 UTC. Psychology Henri Tajfel develops his minimal group paradigm , a constituent of social identity theory. Studies in Animal and Human Behavior, Volume I is published by Konrad Lorenz . Awards Fields Medal Fields Prize in Mathematics Alan Baker mathematician Alan Baker , Heisuke Hironaka , Sergei Novikov mathematician Sergei Novikov and John Griggs Thompson Nobel Prize s Nobel Prize in Physics Physics Hannes Alfv n , Louis N el Nobel Prize in Chemistry Chemistry Luis F. Leloir Nobel Prize in Physiology or Medicine Medicine Bernard Katz , Ulf von Euler , Julius Axelrod Turing Award James H. Wilkinson Births Empty section date July 2010 Deaths January 5 Max Born b. 1882 in science 1882 , physicist and recipient of the Nobel Prize in physics in 1954. August 1 Otto Heinrich Warburg b. 1883 in science 1883 , Germany German physiologist and winner of the 1931 Nobel Prize in Physiology or Medicine . DEFAULTSORT 1970 In Science Category 1970 Science, 1970 In Category 1970 in science fr 1970 en science he 1970 mk 1970 pl 1970 w nauce pt 1970 na ci ncia ru 1970 sv Vetenskaps ret 1970 uk 1970 ... more details
This is a list of people associated with Kyoto University in Japan . Several notable individuals have either studied or worked on the faculty of Kyoto University . Nobel Laureates Hideki Yukawa winner of the Nobel Prize in Physics in 1949 he became the first Japanese to win the Nobel prize Shinichiro Tomonaga winner of the Nobel Prize in Physics Kenichi Fukui winner of the Nobel Prize in Chemistry in 1981 Susumu Tonegawa winner of the Nobel Prize in Physiology or Medicine in 1987 Aung San Suu Kyi winner of the Nobel Prize in Peace in 1991 Ry ji Noyori winner of the Nobel Prize in Chemistry in 2001 Makoto Kobayashi physicist Makoto Kobayashi winner of the Nobel Prize in Physics in 2008 Toshihide Masukawa winner of the Nobel Prize in Physics in 2008 Fields Medalists Heisuke Hironaka mathematician , Fields Medal ists in 1970 Shigefumi Mori mathematician , Fields Medal ists in 1990 Literature Kan Kikuchi Japanese author Motojir Kajii Tatsuji Miyoshi Ooka Shohei Shohei Ooka Yasushi Inoue Akimitsu Takagi crime fiction writer Sakyo Komatsu Keiichiro Hirano Politicians Frank Hsieh aka Hsieh Chang Ting Former mayor of Kaohsiung City and Premier of the Republic of China Premier of Taiwan 2008 Democratic Progressive Party presidential candidate for the Republic of China Taiwan Osachi Hamaguchi Prime Minister of Japan Kijuro Shidehara Prime Minister of Japan Tetsu Katayama Prime Minister of Japan Fumimaro Konoe Prime Minister of Japan Hayato Ikeda Prime Minister of Japan Lee Teng hui Former President of Taiwan Peng Ming Min Taiwan s DPP candidate for the 1996 Taiwan Presidential elections Tadahiro Matsushita five time member of the House of Representatives of Japan Science Kiyoshi Oka mathematician Teiji Takagi mathematician Kinji Imanishi ecologist, anthropologist Motoo Kimura biologist Shinya Yamanaka physician Tetsuro Matsuzawa primatologist Yasutomi Nishizuka biochemist Yasunori Hayashi neuroscientist Makoto Nagao computer scientist, the 21th President of Kyoto University ... more details
7 Hironaka, Heisuke http links.jstor.org sici?sici 0003 486X 28196401 292 3A79 3A1 3C109 3AROSOAA ... to resolve the singularities of all reduced quasi excellent rings. Hironaka 1964 ... more details
In mathematics , an Igusa zeta function is a type of generating function , counting the number of solutions of an equation, modulo p , p sup 2 sup , p sup 3 sup , and so on. Definition For a prime number math p math let math K math be a p adic field , i.e. math K mathbb Q p infty math , math R math the valuation ring and math P math the maximal Ideal ring theory ideal . For math z in K math math operatorname ord z math denotes the valuation of math z math , math mid z mid q operatorname ord z math , and math ac z z pi operatorname ord z math for a uniformizing parameter math pi math of math R math . Furthermore let math phi K n mapsto mathbb C math be a Schwartz Bruhat function , i.e. a locally constant function with compact support and let math chi math be a Character mathematics character of math K math . In this situation one associates to a non constant polynomial math f x 1, ldots, x n in K x 1, ldots,x n math the Igusa zeta function math Z phi s, chi int K n phi x 1, ldots,x n chi ac f x 1, ldots,x n f x 1, ldots,x n s , dx math where math s in mathbb C , operatorname Re s 0, math and math dx math is Haar measure so normalized that math R n math has measure 1. Igusa s theorem Junichi Igusa showed that math Z phi s, chi math is a rational function in math t q s math . The proof uses Heisuke Hironaka s theorem about the resolution of singularities . Later, an entirely different proof was given by Jan Denef using p adic cell decomposition. Little is known, however, about explicit formulas. There are some results about Igusa zeta functions of Fermat varieties . Congruences modulo powers of math P math Henceforth we take math phi math to be the characteristic function of math R n math and math chi math to be the trivial character. Let math N i math denote the number of solutions of the congruence relation congruence math f x 1, ldots,x n equiv 0 mod P i math . Then the Igusa zeta function math Z t int R n f x 1, ldots,x n s , dx math is closely related to the Poinc ... more details
List of Guggenheim fellowship winners for 1971 . United States and Canadian fellows Gar Alperovitz , Lionel R. Bauman Professor of Political Economy, University of Maryland. Norman Birnbaum , University Professor, Georgetown University Law Center. Julie Bovasso , Deceased. Drama. Leo Braudy , University Professor and Bing Professor of English, University of Southern California . Ed Bullins , Playwright, Berkeley, California. Mario A. Bunge , Frothingham Professor of Logic and Metaphysics, McGill University. Robbins Burling , Emeritus Professor of Anthropology and Linguistics, University of Michigan. Noam Chomsky , Institute Professor, Department of Linguistics, M.I.T. John Desmond Clark , Professor Emeritus of Anthropology, University of California, Berkeley. Tom Clark poet Tom Clark , Poet, Berkeley, California. Henry Steele Commager , Deceased. Classics. Robert Coover , T. B. Stowell University Professor, Brown University. Arlene Croce , Dance Critic, Brooklyn, New York. Stillman Drake , Deceased. History of Science. Troy Duster , Associate Professor of Sociology, University of California, Berkeley. Alfred S. Eichner , Deceased. Economics. Dale Eldred , Sculptor, Kansas City Missouri. Charles Fried , Beneficial Professor of Law, Harvard University. Murray Gell Mann , Robert Andrews Millikan Professor Emeritus of Theoretical Physics, California Institute of Technology. Sam Gilliam , Artist, Washington, D.C. Grant Gilmore , Deceased. Law. Nathanael Greene , Professor of History, Wesleyan University. Vartan Gregorian , President, Carnegie Corporation. John J. Gumperz , Emeritus Professor of Anthropology, University of California, Berkeley. Thom Gunn , Poet Retired Senior Lecturer, University of California, Berkeley, San Francisco. Heisuke Hironaka , Professor of Mathematics, Harvard University. Nathan Irvin Huggins , Deceased. U.S. History. Aravind Joshi , Henry Salvatori Professor of Computer and Cognitive Science, University of Pennsylvania . Barbara Kolb , Compose ... more details
of the algebraic variety at the point. Intensive studies of such singularities led in the end to HeisukeHironaka s fundamental theorem on resolution of singularities in birational geometry in characteristic ... At about the same time as Hironaka s work, the catastrophe theory of Ren Thom was receiving ... more details
last Hironaka first Heisuke authorlink Hironaka url http links.jstor.org sici?sici 0003 486X ... of blowings up is functorial with respect to Smooth morphism Smooth morphisms smooth morphisms . Hironaka ... to do explicitly. Hironaka s method Hironaka s method for arbitrary characteristic 0 varieties ... 2008 year2 2009 proved resolution of singularities of 3 folds in all characteristics. Hironaka ... Hironaka 1964 . He proved that it was possible to resolve singularities of varieties over fields ... of the recent proofs are about a tenth of the length of Hironaka s original proof, and are easy enough ... a field of characteristic 0, this follows from Hironaka s theorem, and when X has dimension at most ... Bogomolov first Fedor A. last2 Pantev first2 Tony G. arxiv alg geom 9603019 title Weak Hironaka ... 03 00982 0 home.html title The Hironaka theorem on resolution of singularities or A proof we always ... jams 2005 18 04 S0894 0347 05 00493 5 home.html title Simple Hironaka resolution in characteristic ... conference 2009gcoeopsym index.html Resolution of singularities I , a video of a talk by Hironaka ... more details
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