Abstract
Mathematical works of Hiroshi Umemura
Highlights
Hiroshi Umemura was born in 1944 at Aichi prefecture in Japan
In the 1970s he studied algebraic geometry, especially on vector bundles over abelian varieties and maximal connected algebraic groups contained in the Cremona group Autkk(x1, x2, . . . , xn)
The classification of the Fano varieties were reconsidered after their construction. When he visited Strasbourg in 1984, he analyzed Painlevé’s Leçons de Stockholm [8] in detail and he unveiled Painlevé’s theory on irreducibility of nonlinear differential equations. He gave a rigorous definition of classical functions, which are reduced to known functions, such as abelian functions or solutions of linear equations, in terms of the differential Galois theory based on Grothendieck’s scheme theory
Summary
Hiroshi Umemura was born in 1944 at Aichi prefecture in Japan. In 1967 he graduated from Nagoya University, where he spent most of his career. When he visited Strasbourg in 1984, he analyzed Painlevé’s Leçons de Stockholm [8] in detail and he unveiled Painlevé’s theory on irreducibility of nonlinear differential equations He gave a rigorous definition of classical functions, which are reduced to known functions, such as abelian functions or solutions of linear equations, in terms of the differential Galois theory based on Grothendieck’s scheme theory. After a fierce struggle against long papers by Vessiot, Umemura constructed an infinite dimensional Galois theory in a rigorous framework His infinite Galois theory is one of the most successful differential Galois theories which go beyond classical differential Galois theories in finite dimensions, such as the Picard–Vessiot theory and Kolchin’s theory. He received the MSJ Algebra Prize in 1998 for his study of the Painlevé equations and differential Galois theory from the Mathematical Society of Japan He published 55 papers and two Japanese books. The authors would like to express our gratitude to Shigeru Mukai for helpful comments and advice
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