- Kunihiko Kodaira
name =Kunihiko Kodaira
birth_date =Birth date|1915|03|16
death_date =Death date and age|1997|07|26|1915|03|16
Institute for Advanced Study
University of Tokyo
doctoral_advisor =Shokichi Iyanaga
Algebraic geometry, complex manifolds
Fields Medal(1954) Wolf Prize(1984/5)
nihongo|Kunihiko Kodaira|小平 邦彦|Kodaira Kunihiko|
16 March, 1915– 26 July, 1997was a Japanese mathematicianknown for distinguished work in algebraic geometryand the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medalin 1954, being the first Japanese to receive this honour.
He was born in
Tokyo. He graduated from the University of Tokyoin 1938 with a degree in mathematics and also graduated from the physics department at the University of Tokyoin 1941. During the war years he worked in isolation, but was able to master Hodge theoryas it then stood. He obtained his Ph.D.degree from the University of Tokyoin 1949, with a thesis entitled "Harmonic fields in Riemannian manifolds". He was involved in cryptographic work from about 1944, at a time of great personal difficulty, while holding an academic post in Tokyo.
Institute for Advanced Study
In 1949 he travelled to the
Institute for Advanced Studyin Princeton, New Jerseyat the invitation of Hermann Weyl. At this time the foundations of Hodge theory were being brought in line with contemporary technique in operator theory. Kodaira rapidly became involved in exploiting the tools it opened up in algebraic geometry, adding sheaf theoryas it became available. This work was particularly influential, for example on Hirzebruch.
In a second research phase, Kodaira wrote a long series of papers in collaboration with
D. C. Spencer, founding the deformation theoryof complex structures on manifolds. This gave the possibility of constructions of moduli spaces, since in general such structures depend continuously on parameters. It also identified the sheaf cohomology groups, for the sheaf associated with the holomorphic tangent bundle, that carried the basic data about the dimension of the moduli space, and obstructions to deformations. This theory is still foundational, and also had an influence on the (technically very different) scheme theoryof Grothendieck. Spencer then continued this work, applying the techniques to structures other than complex ones, such as G-structures.
In a third major part of his work, Kodaira worked again from around 1960 through the
classification of algebraic surfaces, from birational geometry, from the point of view of complex manifold theory. This resulted in a typology of seven kinds of two-dimensional compact complex manifolds, recovering the five algebraic types known classically; the other two being non-algebraic. He provided also detailed studies of elliptic fibrations of surfaces over a curve, or in other language elliptic curves over function fields, a theory whose arithmetic analogue proved important soon afterwards. This work also included a characterisation of K3 surfaces as deformations of quartic surfaces in "P"4, and the theorem that they form a single diffeomorphismclass. Again, this work has proved foundational. (The K3 surfaces were named after Kummer, Kähler, and Kodaira).
Kodaira left the Institute for Advanced Study in 1961, and briefly served as chair at the
Johns Hopkins Universityand Stanford UniversityIn 1967, returned to the University of Tokyo. He was awarded a Wolf Prizein 1984/5. He died in Kofuon 26 July, 1997.
Spectral theory of ordinary differential equations
Kodaira vanishing theorem
Kodaira embedding theorem
NAME= Kodaira, Kunihiko
DATE OF BIRTH=
March 16, 1915
PLACE OF BIRTH=
DATE OF DEATH=
July 26, 1997
PLACE OF DEATH=
Kōfu, Yamanashi, Japan
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