Kodaira Kunihiko

Kunihiko Kodaira (1969)

Kodaira Kunihiko ( Japanese 小平 邦彦 ; born March 16, 1915 in Tokyo Prefecture , † July 26, 1997 in Kofu ) was a Japanese mathematician who was awarded the Fields Medal in 1954 for outstanding services to mathematics .

Life

Kodaira's father was an agronomist and temporarily vice minister of agriculture in Japan. Kodaira graduated from the Imperial University of Tokyo in mathematics in 1938 and in physics in 1941. 1944-1951 he was associate professor of physics in Tokyo. At that time ( World War II ) Japan was largely isolated and it was not possible for Japanese scientists to maintain contact with other scientists in the world. Kodaira, however, found a way to continue reading the publications of Hermann Weyl , Marshall Stone , John von Neumann , William Hodge , André Weil and Oscar Zariski , as well as to publish his own work.

In 1949 he published Harmonic fields in Riemannian manifolds-generalized potential theory in the prestigious Annals of Mathematics , which caught the attention of Weyl and Donald Spencer and led to an invitation to Princeton . From 1949 to 1961, Kodaira was a member of the Institute for Advanced Study at Princeton. In 1961/62 he spent a year at Harvard University . In 1962 he got a chair in mathematics at Johns Hopkins University , in 1965 he took a chair in mathematics at Stanford University . In 1967 Kodaira left Stanford and returned to Japan, where he also received a chair in mathematics at the University of Tokyo.

Kodaira's work covered many subjects within mathematics. His main work lay in the area of ​​differential equations (where he was influenced by Weyl), the theory of harmonic integrals (Hodge theory) and their application in algebraic geometry. In the 1960s he dealt with the classification of compact complex-analytic surfaces (Kodaira dimension, etc.), providing the work of the Italian school of algebraic geometry with strict proofs and greatly expanding them. During his time at Princeton he worked with Friedrich Hirzebruch and his long-time collaborator (from 1949) Donald Spencer (Kodaira-Spencer theory, deformation of complex structures).

In his embedding theorem he showed that compact Kähler manifolds , in which the metric is not only compatible with a Kähler form , but a Hodge metric , can be analytically embedded in a projective (complex) space, in other words they are in complex by homogeneous polynomials Variables defined. Conversely, since projective algebraic varieties are also Hodge varieties, the theorem can also be formulated in such a way that compact Hodge manifolds and projective algebraic varieties are isomorphic in the complex. But there are also Kähler manifolds that are not Hodge manifolds, for example certain complex tori. Kodaira showed for two-dimensional manifolds that compact Kahler manifolds can be deformed into algebraic varieties and hypothesized that the same is true in higher dimensions. Here, however, Claire Voisin found a counterexample.

Among his students are Walter Baily and (in his own words) Friedrich Hirzebruch , who was at the Institute for Advanced Study from 1952 to 1954 . Both were later close friends of Kodaira.

He was married to Seiko, a sister of the mathematician Iyanaga .

Kodaira became an honorary member of many learned societies; Particularly noteworthy is the membership in the London Mathematical Society (London Mathematical Society, 1979) and the award of the Fields Medal in 1954 (at Weyl's special instigation). In 1957 he was awarded the Japanese Order of Culture . He was also a member of the National Academy of Sciences (since 1975), the American Academy of Arts and Sciences (since 1978), the Academy of Sciences in Göttingen and the Japanese Academy of Sciences .

His PhD students include Walter Baily and James Morrow .

In 1998 the asteroid (6964) Kunihiko was named after him.

Fonts

• Complex Manifolds and Deformation of Complex Structures , Springer-Verlag, Grundlehren der Mathematischen Wissenschaften 283, 1986, reprint 2004 (Classics in Mathematics), ISBN 3-540-22614-1 (with appendix by Daisuke Fujiwara)
• Introduction to Complex Analysis , Cambridge University Press, 1985, ISBN 0-521-24391-2 .
• Complex Analysis , Cambridge Studies in Advanced Mathematics 107, Cambridge University Press, 2007 ISBN 0-521-80937-1 .
• With James Morrow: Complex manifolds , New York: Holt, Rinehart and Winston 1971, AMS Chelsea Publishing 2006.
• Kunihiko Kodaira: Collected Works , 3 vols., Iwanami Shoten, Princeton University Press, 1975 (Ed. And foreword Walter Baily).

literature

• S. Noma (Ed.): Kodaira Kunihiko . In: Japan. An Illustrated Encyclopedia. Kodansha, 1993, ISBN 4-06-205938-X , p. 804.
• Biography in Encyclopaedia Britannica .
• Hermann Weyl: Fields medal laudation on Kodaira, Proc. ICM 1954, vol. 1, p. 161.

See also

• Kodaira Disappearance Law

Web links

• John J. O'Connor, Edmund F. Robertson :  Kunihiko Kodaira. In: MacTutor History of Mathematics archive .
• Literature by and about Kodaira Kunihiko in the catalog of the German National Library
• Hirzebruch zu Kodaira, Notices AMS 1998, PDF, English
• Obituary Donald Spencer, Notices AMS 1998, PDF, English
• Some of Kodaira's work in the Proc.Nat.Acad. USA are online here: [1]

Individual evidence

1. ↑ In the Hodge metric, the periods of the underlying (1,1) form are whole numbers. The corresponding manifolds are then called Hodge manifolds. Examples are the Fubini Study metrics on projective spaces.
2. ↑ According to Chow's theorem one can infer from projective to algebraic
3. ^ Mathematics Genealogy Project
4. ↑ Minor Planet Circ. 32347
5. ↑ Review by Sommese , BAMS, 16, 1987, 308-310

Japanese name: As is common in Japan, the family name comes before the first name in this article . Thus Kodaira is the family name, Kunihiko the first name.