COMPLEX ANALYSIS KUNIHIKO KODAIRA PDF

Parts of it could be used for a graduate complex manifolds course. Most of all it is a piece of work which shows mathematics as lying somewhere between discovery and invention, a fact which all mathematicians know, but most inexplicably conceal in their work. He graduated twice from the University of Tokyo, with a degree in mathematics in and one in physics in From until , Kodaira was an associate professor at the University of Tokyo but by this time his work was well known to mathematicians worldwide and in he accepted an invitation from H.

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Early years Edit Kodaira was born in Tokyo. He graduated from the University of Tokyo in with a degree in mathematics and also graduated from the physics department at the University of Tokyo in During the war years he worked in isolation, but was able to master Hodge theory as it then stood.

He obtained his Ph. He was involved in cryptographic work from about , while holding an academic post in Tokyo. He was subsequently also appointed Associate Professor at Princeton University in and promoted to Professor in 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 Friedrich Hirzebruch. In a second research phase, Kodaira wrote a long series of papers in collaboration with Donald 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 through the classification of algebraic surfaces from the point of view of birational geometry of complex manifolds.

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 algebraic 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 P4, and the theorem that they form a single diffeomorphism class. Again, this work has proved foundational. In , returned to the University of Tokyo. He died in Kofu on 26 July

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Kunihiko Kodaira

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