Kunihiko Kodaira | |
|---|---|
 | |
| Born | (1915-03-16)March 16, 1915 |
| Died | July 26, 1997(1997-07-26) (aged 82) |
| Nationality | Japanese |
| Alma mater | University of Tokyo |
| Known for | Algebraic geometry,complex manifolds,Hodge theory |
| Awards | Fields Medal (1954) Japan Academy Prize (1957) Order of Culture (1957) Wolf Prize (1984/5) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Tokyo Institute for Advanced Study Johns Hopkins University Princeton University Stanford University |
| Doctoral advisor | Shokichi Iyanaga |
| Doctoral students | Walter Lewis Baily, Jr. Shigeru Iitaka Yoichi Miyaoka James A. Morrow |
Kunihiko Kodaira (小平 邦彦,Kodaira Kunihiko,Japanese pronunciation:[kodaꜜiɾakɯɲiꜜçi̥ko], 16 March 1915 – 26 July 1997) was a Japanesemathematician known for distinguished work inalgebraic geometry and the theory ofcomplexmanifolds, and as the founder of the Japanese school of algebraic geometers.[1] He was awarded aFields Medal in 1954, being the first Japanese national to receive this honour.[1]
Kodaira was born inTokyo. He graduated from theUniversity of Tokyo in 1938 with a degree in mathematics and also graduated from the physics department at the University of Tokyo in 1941. During thewar years he worked in isolation, but was able to masterHodge theory as it then stood. He obtained hisPhD from theUniversity of Tokyo in 1949, with a thesis entitledHarmonic fields in Riemannian manifolds.[2] He was involved incryptographic work from about 1944, while holding an academic post in Tokyo.
In 1949 he travelled to theInstitute for Advanced Study inPrinceton, New Jersey at the invitation ofHermann Weyl. He was subsequently also appointed Associate Professor atPrinceton University in 1952 and promoted to Professor in 1955. At this time the foundations of Hodge theory were being brought in line with contemporary technique inoperator theory. Kodaira rapidly became involved in exploiting the tools it opened up in algebraic geometry, addingsheaf theory as it became available. This work was particularly influential, for example onFriedrich Hirzebruch.
In a second research phase, Kodaira wrote a long series of papers in collaboration withDonald C. Spencer, founding thedeformation theory of complex structures on manifolds. This gave the possibility of constructions ofmoduli spaces, since in general such structures dependcontinuously on parameters. It also identified thesheaf cohomology groups, for the sheaf associated with theholomorphic 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 ofGrothendieck. Spencer then continued this work, applying the techniques to structures other than complex ones, such asG-structures.
In a third major part of his work, Kodaira worked again from around 1960 through theclassification of algebraic surfaces from the point of view ofbirational geometry of complex manifolds. This resulted in a typology of seven kinds of two-dimensionalcompact complex manifolds, recovering the five algebraic types known classically; the other two being non-algebraic. He provided also detailed studies ofelliptic fibrations of surfaces over a curve, or in other languageelliptic curves overalgebraic function fields, a theory whose arithmetic analogue proved important soon afterwards. This work also included a characterisation ofK3 surfaces as deformations ofquartic surfaces inP3, and the theorem that they form a singlediffeomorphism class. Again, this work has proved foundational. (The K3 surfaces were named afterErnst Kummer,Erich Kähler, and Kodaira).
Kodaira left Princeton University and the Institute for Advanced Study in 1961, and briefly served as chair at theJohns Hopkins University andStanford University. In 1967, he returned to theUniversity of Tokyo. He was awarded aWolf Prize in 1984/5. He died inKofu on 26 July 1997.
He was honoured with the membership of theJapan Academy, theMathematical Society of Japan and theAmerican Academy of Arts and Sciences in 1978. He was the foreign associate of the USNational Academy of Sciences in 1975, member of theGöttingen Academy of Sciences in 1974 and honorary member of theLondon Mathematical Society in 1979. He received the Order of Culture and theJapan Academy Prize in 1957 and the Fujiwara Prize in 1975.
