Kunihiko Kodaira
Kunihiko Kodaira (Japanese小平 邦彦; born March 16, 1915 in the prefecture of Tokyo, † 26 July 1997 Kōfu ) was a Japanese mathematician who in 1954 was awarded for special achievements in mathematics with the Fields Medal.
Life
His father was an agronomist and sometimes vice minister for agriculture in Japan. Kodaira graduated 1938 at the Tokyo Imperial University in mathematics and physics in 1941. 1944-1951 he was associate professor of physics in Tokyo. At this 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 upright. Kodaira, however, found a way to continue the publication of Hermann Weyl, Marshall Stone, John von Neumann, William Hodge, André Weil and Oscar Zariski to get read to, and to publish his own work.
In 1949 he published in the prestigious Annals of Mathematics Harmonic fields in Riemannian work - manifolds generalized potential theory, which caught the attention of Weyl and Spencer and led to an invitation to Princeton. From 1949 to 1961 Kodaira was a member of the Institute for Advanced Study at Princeton. 1961/62 he spent a year at Harvard University. In 1962 he was a professor of mathematics at Johns Hopkins University, in 1965 he accepted a chair of mathematics at Stanford University. 1967 left Kodaira Stanford and returned to Japan, where he also became professor of mathematics at the University of Tokyo.
The work of Kodaira covered many topics within mathematics. His main works were in the range of the differential equations (where he was influenced by Weyl ), the theory of harmonic integrals ( Hodge theory ) and their applications in algebraic geometry. In the 1960s he busied himself with the classification of compact complex - analytic surfaces ( Kodaira dimension, etc.), where he knew the works of the Italian school of algebraic geometry with rigorous proofs and greatly expanded. During his time at Princeton, he worked with Friedrich Hirzebruch and his longtime 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 not only has Kählerform but a Hodge metric is analytic in a projective (complex) space can be embedded, in other words, they are defined by homogeneous polynomials in complex variables. As vice versa are also projective algebraic varieties Hodge varieties, can also formulate the proposition that in the complex compact Hodge manifolds and projective algebraic varieties are isomorphic. But there are also Kähler manifolds that are not Hodge manifolds, for example, certain complex tori. Kodaira showed for two - dimensional manifolds that compact Kähler manifolds can be deformed into algebraic varieties, and suspected that the same is true in higher dimensions. Here, however, took Claire Voisin a counterexample.
Among his students is one of Walter Baily and ( according to its own words ) Friedrich Hirzebruch, who was from 1952-4 at the Institute for Advanced Study. Both were later close friends of Kodaira.
He was married to Seiko, a sister of the mathematician Iyanaga.
Kodaira was an honorary member of many learned societies; particularly worthy of mention is a member of the London Mathematical Society ( London Mathematical Society, 1979) and the award of the Fields Medal in 1954 ( at the specific operation of Weyl ).
His doctoral include Walter Baily and James Morrow.
Writings
- Complex Manifolds and Deformation of Complex Structures. Springer -Verlag, Heidelberg 2004, ISBN 3-540-22614-1.
- Introduction to Complex Analysis. Cambridge University Press, 1985, ISBN 0-521-24391-2.
- Complex Analysis. Cambridge University Press, ISBN 0-521-80937-1.
- With Morrow: Complex manifolds 1971.
- Kunihiko Kodaira: Collected Works, 3 vols, Iwanami Shoten, Princeton University Press, 1975 ( ed. and preface Walter Baily ).