Shigefumi Mori

Shigefumi Mori ( 森 重 文 , Mori Shigefumi, born

February 23, 1951) is a Japanese mathematician, Shigefumi Mori
known for his work in algebraic geometry, particularly
in relation to the classification of three-folds. He won
the Fields Medal in 1990.

Career
Mori completed his Ph.D. titled "The Endomorphism
Rings of Some Abelian Varieties" under Masayoshi
Nagata at Kyoto University in 1978.[1] He was a
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 Born February 23, 1951
since 1990. Nagoya, Japan
Nationality Japanese
Alma mater Kyoto University
Work Known for Algebraic geometry
minimal model program
Keel–Mori theorem
Awards Fields Medal (1990)
Cole Prize (1990)
Scientific career
Fields Mathematician
Institutions Nagoya University
With Edward Witten (1990) Kyoto University
Thesis The Endomorphism Rings of
He generalized the classical approach to the Some Abelian Varieties (1978)
classification of algebraic surfaces to the classification Doctoral Masayoshi Nagata
of algebraic three-folds. The classical approach used advisor
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 Mori's 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.[2]

Awards
He was awarded the Fields Medal in 1990 at the International Congress of Mathematicians.

In 2021, he received the Order of Culture.[3]

Major publications
Mori, Shigefumi (1979). "Projective Manifolds with Ample
Tangent Bundles". Annals of Mathematics. 110 (3): 593–
606. doi:10.2307/1971241 (https://doi.org/10.2307%2F197
1241). JSTOR 1971241 (https://www.jstor.org/stable/19712
41).
Mori, Shigefumi; Mukai, Shigeru (1981). "Classification of
Fano 3-folds with B2 ≥ 2". Manuscripta Mathematica. 36
(2): 147–162. doi:10.1007/BF01170131 (https://doi.org/10.1
007%2FBF01170131). S2CID 189831516 (https://api.sema Mori attended the opening
nticscholar.org/CorpusID:189831516). ceremony of the International
Congress of Mathematicians
Mori, Shigefumi; Mukai, Shigeru (2003). "Classification (2018)
of Fano 3-folds with B2 ≥ 2. (Erratum)". Manuscripta
Mathematica. 110 (3): 407. doi:10.1007/s00229-002-
0336-2 (https://doi.org/10.1007%2Fs00229-002-0336-2). S2CID 121266346 (https://api.
semanticscholar.org/CorpusID:121266346).
Mori, Shigefumi (1982). "Threefolds Whose Canonical Bundles Are Not Numerically
Effective". Annals of Mathematics. 116 (1): 133–176. doi:10.2307/2007050 (https://doi.org/1
0.2307%2F2007050). JSTOR 2007050 (https://www.jstor.org/stable/2007050).
Mori, Shigefumi (1988). "Flip theorem and the existence of minimal models for 3-folds" (http
s://doi.org/10.1090%2FS0894-0347-1988-0924704-X). Journal of the American
Mathematical Society. 1 (1): 117–253. doi:10.1090/S0894-0347-1988-0924704-X (https://do
i.org/10.1090%2FS0894-0347-1988-0924704-X). JSTOR 1990969 (https://www.jstor.org/sta
ble/1990969).
Kollár, János; Miyaoka, Yoichi; Mori, Shigefumi. Rationally connected varieties. J. Algebraic
Geom. 1 (1992), no. 3, 429–448.
Kollár, János; Miyaoka, Yoichi; Mori, Shigefumi (1992). "Rational connectedness and
boundedness of Fano manifolds" (https://doi.org/10.4310%2Fjdg%2F1214453188). Journal
of Differential Geometry. 36 (3). doi:10.4310/jdg/1214453188 (https://doi.org/10.4310%2Fjd
g%2F1214453188). S2CID 118102421 (https://api.semanticscholar.org/CorpusID:11810242
1).
Kollár, János; Mori, Shigefumi (1992). "Classification of three-dimensional flips" (https://doi.o
rg/10.1090%2FS0894-0347-1992-1149195-9). Journal of the American Mathematical
Society. 5 (3): 533–703. doi:10.1090/S0894-0347-1992-1149195-9 (https://doi.org/10.109
0%2FS0894-0347-1992-1149195-9). JSTOR 2152704 (https://www.jstor.org/stable/215270
4).
Keel, Sean; Mori, Shigefumi (1997). "Quotients by Groupoids". Annals of Mathematics. 145
(1): 193–213. doi:10.2307/2951828 (https://doi.org/10.2307%2F2951828). JSTOR 2951828
 (https://www.jstor.org/stable/2951828). S2CID 17830187 (https://api.semanticscholar.org/Co
rpusID:17830187).
Kollár, János; Mori, Shigefumi. Birational geometry of algebraic varieties. With the
collaboration of C. H. Clemens and A. Corti. Translated from the 1998 Japanese original.
Cambridge Tracts in Mathematics, 134. Cambridge University Press, Cambridge, 1998.
viii+254 pp. ISBN 0-521-63277-3

See also
Keel–Mori theorem

References
1. Shigefumi Mori (https://mathgenealogy.org/id.php?id=100894) at the Mathematics
Genealogy Project
2. "Kyoto University professor elected head of International Mathematical Union" (http://www.ja
pantimes.co.jp/news/2014/08/12/national/kyoto-university-professor-elected-head-internatio
nal-mathematical-union/). The Japan Times Online. 2014-08-12.
3. "長嶋茂雄さんら9人文化勲章 功労者に加山雄三さんら" (https://www.jiji.com/jc/article?k=20
21102600557&g=pol). Jiji.com. Retrieved October 26, 2021.
O'Connor, John J.; Robertson, Edmund F., "Shigefumi Mori" (https://mathshistory.st-andrew
s.ac.uk/Biographies/Mori.html), MacTutor History of Mathematics Archive, University of St
Andrews
Heisuke Hironaka, The work of Shigefumi Mori. (https://books.google.com/books?id=q6eSjV
-0egUC&pg=PA487) Fields Medallists Lectures, Michael F. Atiyah (Editor), Daniel Iagolnitzer
(Editor); World Scientific Publishing, 2007. ISBN 981-02-3117-2

External links

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