Shigefumi Mori

Native spelling: 森重文

fl. 1951, Nagoya, Japan

GeometryAlgebraFields Medal 1990

Japanese algebraic geometer who founded the minimal model program through the cone theorem and bend-and-break techniques; awarded the Fields Medal in 1990.

Shigefumi Mori was born in Nagoya in 1951 and spent essentially his entire career at Kyoto University, where he studied under Masayoshi Nagata, received his doctorate in 1978, and became a professor at the Research Institute for Mathematical Sciences (RIMS).

His first landmark result, in 1979, proved the Hartshorne conjecture: projective space is the only smooth projective variety with ample tangent bundle. The proof, over fields of arbitrary characteristic, introduced the bend-and-break method — producing rational curves by deformation and degeneration — which became the engine of his later work. In the 1980s he proved the cone and contraction theorems and, building on them, completed the minimal model program for threefolds, including the existence of three-dimensional flips (1988). For this he received the Fields Medal at the 1990 ICM in Kyoto.

Mori remained at the center of birational geometry: the program he launched was later extended to all dimensions (with key steps by Birkar, Cascini, Hacon and McKernan), and his book with János Kollár, 'Birational Geometry of Algebraic Varieties', is the standard introduction to the field. He served as president of the International Mathematical Union from 2015 to 2018 and received Japan's Order of Culture in 2021.

Workplaces: Research Institute for Mathematical Sciences, Kyoto University

Japan

Award-winning work

Fields Medal 1990Mori created the minimal model program, a systematic way to simplify algebraic varieties by birational surgery. His breakthrough was the cone theorem: the cone of curves of a smooth projective variety is rationally polyhedral in the region where the canonical divisor fails to be numerically effective, with extremal rays generated by rational curves. To detect these rays he invented 'bend-and-break' arguments showing that rational curves deform until they split. Contracting extremal rays gives a sequence of flips and divisorial contractions that conjecturally reduces every variety to a minimal model or a fibration by Fano varieties. The program, completed in dimension three by Mori and others and later in all dimensions for important classes, transformed birational geometry.

Contributions, linked to the library

Library topicAlgebraic geometryFounder of the minimal model program, the central organizing framework of modern birational algebraic geometry.