ⓘ Shigefumi Mori

Shigefumi Mori

ⓘ Shigefumi Mori

Shigefumi Mori is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds.


1. Career

Mori completed his PhD titled "The Endomorphism Rings of Some Abelian Varieties" under Masayoshi Nagata at Kyoto University in 1978. He was visiting professor at Harvard University during 1977–1980, the Institute for Advanced Study in 1981–82, Columbia University 1985–87 and the University of Utah for periods during 1987–89 and again during 1991–92. He has been a professor at Kyoto University since 1990.


2. Work

He generalized the classical approach to the classification of algebraic surfaces to the classification of algebraic three-folds. The classical approach used the concept of minimal models of algebraic surfaces. He found that the concept of minimal models can be applied to three-folds as well if we allow some singularities on them. The extension of Moris results to dimensions higher than three is called the minimal model program and is an active area of research in algebraic geometry.

He has been elected president of the International Mathematical Union, becoming the first head of the group from East Asia.


3. Selected publications

  • Mori, Shigefumi 1979. "Projective manifolds with ample tangent bundles". Ann. of Math. 110 3: 593–606. doi:10.2307/1971241. JSTOR 1971241. MR 0554387.
  • Mori, Shigefumi 1988. "Flip theorem and existence of minimal models for 3-folds". J. Amer. Math. Soc. 1 1: 117–253. doi:10.2307/1990969. JSTOR 1990969. MR 0924704.
  • Mori, Shigefumi 1982. "Threefolds whose canonical bundles are not numerically effective". Ann. of Math. 116 1: 133–176. doi:10.2307/2007050. JSTOR 2007050. MR 0662120. PMC 349565. PMID 16592836.
  • PhD, Araujo developed techniques related to Japanese mathematician Shigefumi Mori s proposed theory of rational curves of minimal degree, which she published
  • 93 163, doi: 10.2307 1971417, ISSN 0003 - 486X, JSTOR 1971417, MR 0924674 Mori Shigefumi 1985 On 3 - dimensional terminal singularities Nagoya Mathematical
  • Tomisaku Kawasaki 1990 80th Koji Nakanishi Masahiko Aoki Shigeru Iitaka, Shigefumi Mori Yujiro Kawamata Satoshi Ōmura 1989 79th Sengaku Mayeda Masatoshi
  • University Press, ISBN 978 - 1 - 107 - 03534 - 8, MR 3057950 Kollar, Janos Mori Shigefumi 1998 Birational Geometry of Algebraic Varieties, Cambridge University
  • flips where the existence of three - dimensional flips first proved by Shigefumi Mori was established in a more general log setting. The inductive method
  • 141I, doi: 10.1070 SM1971v015n01ABEH001536, MR 0291172 Kollar, Janos Mori Shigefumi 1998 Birational Geometry of Algebraic Varieties, Cambridge University
  • sheaves. Compositio Math. 41 1980 no. 1, 39 60. Kollar, Janos Mori Shigefumi 1998 Birational geometry of algebraic varieties, Cambridge Tracts
  • Kluwer Academic Publishers, ISBN 978 - 1 - 55608 - 010 - 4 Fujino, Osamu Mori Shigefumi 2000 A canonical bundle formula Journal of Differential Geometry
  • researching and teaching at the university. It includes one Fields Medalist. Shigefumi Mori one of the 1990 Fields Medalists, spent most of his academic career
  • birational geometry by Shigefumi Mori to study the existence of rational curves on varieties. For a Fano variety of positive dimension Mori showed that there

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