left|120px

'''Kunihiko Kodaira '''(小平  邦彦, variétés complexes et aussi en tant que fondateur de l'école japonaise de géomètrie algébrique. Il a reçu une médaille Fields en 1954, le premier Japonais à avoir cet honneur. Il est né à Tōkyō.  

Ses premiers travaux étaient pour la plupart en analyse fonctionnelle. Pendant les années de guerre, il a travaillé seul, mais a pu maîtriser la théorie de Hodge.  Il a écrit son doctorat sur ce sujet, soutenu en 1949. Il avait été impliqué dans le travail cryptographique en 1944, tout en ayant un poste académique à Tokyo.

En 1949, il a fait un séjour à l'IAS à Princeton, à l'invitation de Hirzebruch.

Dans une deuxième série de recherches, Kodaira a écrit une longue suite d'articles en collaboration avec espaces de modules, puisqu'en général de telles structures dépendent des paramètres continus.  Il a également identifié les groupes de cohomologie des faisceaux, pour le faisceau lié au fibré tangent holomorphe, ce qui a fourni les données de base au sujet de la dimension de l'espace de modules, et des obstructions aux déformations.  Cette théorie est encore fondamentale, et a également eu une influence sur la  théorie des schémas de Grothendieck. Spencer a alors poursuivi ce travail, appliquant ces techniques aux structures autres que la structure complexe, comme par exemple les G-structures.

{{Infobox Scientist 
 |name              =Kunihiko Kodaira
 |box_width         =
 |image             =Kodaira Kunihiko.jpg
 |image_width       =
 |caption           =
 |birth_date        =
 |birth_place       =Tokyo, Japan
 |death_date        =
 |death_place       =Kōfu, Japan
 |residence         =
 |citizenship       =
 |nationality       =
 |ethnicity         =
 |field             =Mathematics
 |work_institutions =Institute for Advanced Study
 |alma_mater        =University of Tokyo
 |doctoral_advisor  =Shokichi Iyanaga
 |doctoral_students =
 |known_for         =Algebraic geometry, complex manifolds
 |author_abbrev_bot =
 |author_abbrev_zoo =
 |influences        =
 |influenced        =
 |prizes            =Fields Medal (1954)<br>Wolf Prize (1984/5)
 |footnotes         =
 |signature         = 
}}

 was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medal in 1954, being the first Japanese to receive this honour. 

== Early years ==
He was born in war years he worked in isolation, but was able to master Hodge theory as it then stood.  He obtained his Ph.D. degree from the University of Tokyo in 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 Study in Princeton, New Jersey at 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 theory as 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 theory of 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 theory of 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 Kummer, Kähler, and Kodaira). 

==Later years==
Kodaira left the Institute for Advanced Study in 1961, and briefly served as chair at the Johns Hopkins University and Stanford University  In 1967, returned to the University of Tokyo. He was awarded a Wolf Prize in 1984/5. He died in Kofu on 26 July, 1997.