Kunihiko Kodaira

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Kunihiko Kodaira

Born

March 16, 1915

, Japan

Died

July 26, 1997

(aged 82)

Alma mater

Known for

Awards

(1954)

(1957)

(1984/5)

Scientific career

Fields

Institutions

Doctoral

students

Kunihiko Kodaira

(

小平邦彦

Kodaira Kunihiko

;

Japanese pronunciation:

, 16 March 1915 – 26 July 1997)

was a Japanese

known for distinguished work in

and the

theory of

, and as the founder of the Japanese school of

algebraic geometers.

He was awarded a

in 1954, being the first

Japanese national to receive this honour.

Early life and education

[

]

Kodaira was born in

. He graduated from the

in 1938

with a degree in mathematics and also graduated from the physics department at

the University of Tokyo in 1941. During the

years he worked in isolation,

but was able to master

as it then stood.

He obtained his

from

the

in 1949, with a thesis entitled

Harmonic fields in

Riemannian manifolds

He was involved in

work from about

1944, while holding an academic post in Tokyo.

Institute for Advanced Study and Princeton

University

[

]

In 1949 he travelled to the

at the invitation of

. He was subsequently also appointed

Associate Professor at

in 1952 and promoted to Professor

in 1955.

At this time the foundations of Hodge theory were being brought in

line with contemporary technique in

. Kodaira rapidly became

involved in exploiting the tools it opened up in algebraic geometry, adding

as it became available. This work was particularly influential,

for example on

In a second research phase, Kodaira wrote a long series of papers in collaboration with

, founding

the

of complex structures on manifolds. This gave the possibility of constructions of

, since in general such structures depend

on parameters. It also identified the

, for the sheaf associated with the

, 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)

. Spencer then continued this work, applying the

techniques to structures other than complex ones, such as

In a third major part of his work, Kodaira worked again from around 1960 through the

from the point of view of

of complex manifolds. This resulted in a typology of seven

kinds of two-dimensional

complex manifolds, recovering the five algebraic types known classically; the other

two being non-algebraic. He provided also detailed studies of

of surfaces over a curve, or in

other language

over

, a theory whose arithmetic analogue proved important

soon afterwards. This work also included a characterisation of

as deformations of

and the theorem that they form a single

class. Again, this work has proved foundational.

(The K3

surfaces were named after

, and Kodaira).

Later years

[

]

Kodaira left Princeton University and the Institute for Advanced Study in 1961, and briefly served as chair at the

and

In 1967, he returned to the

. He was awarded a

in 1984/5. He died in

on 26 July 1997.

He was honoured with the membership of the

, the

and the

in 1978. He was the foreign associate of the US

in 1975, member of

the

Academy of Sciences in 1974 and honorary member of the

in 1979. He received

the Order of Culture and the

in 1957 and the Fujiwara Prize in 1975.

Bibliography

[

]

; Kodaira, Kunihiko (2006) [1971],

, AMS Chelsea Publishing, Providence, RI,

Kodaira, Kunihiko (1975),

(ed.),

Kunihiko Kodaira: collected works

, vol. I, Iwanami Shoten,

Publishers, Tokyo; Princeton University Press, Princeton, N.J.,

Kodaira, Kunihiko (1975), Baily, Walter L. (ed.),

, vol. II, Iwanami Shoten,

Publishers, Tokyo; Princeton University Press, Princeton, N.J.,

Kodaira, Kunihiko (1975), Baily, Walter L. (ed.),

Kunihiko Kodaira: collected works

, vol. III, Iwanami Shoten,

Publishers, Tokyo; Princeton University Press, Princeton, N.J.,

Kodaira, Kunihiko (2005) [1981],

, Classics in

Mathematics, Berlin, New York:

Kodaira, Kunihiko (2007),

Complex analysis

, Cambridge Studies in Advanced Mathematics, vol. 107,