Kunihiko Kodaira (小平 邦彦 Kodaira Kunihiko, 16 March 1915 – 26 July 1997) 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. He was born in Nagano Prefecture. March 16 is the 75th day of the year in the Gregorian Calendar (76th in Leap years). ... 1915 was a common year starting on Friday (see link for calendar). ... July 26 is the 207th day (208th in leap years) of the year in the Gregorian Calendar, with 158 days remaining. ... 1997 is a common year starting on Wednesday of the Gregorian calendar. ... A mathematician is a person whose area of study and research is mathematics. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... In differential geometry, a complex manifold is a manifold such that every neighborhood looks like the complex n-space. ... The Fields Medal is a prize awarded to up to four mathematicians (not over forty years of age) at each International Congress of International Mathematical Union, since 1936 and regularly since 1948 at the initiative of the Canadian mathematician John Charles Fields. ... 1954 was a common year starting on Friday of the Gregorian calendar. ... Nagano Prefecture (長野県; Nagano-ken) is located on Honshu island, Japan. ...

His early work was mostly in functional analysis. During the war years he worked in isolation, but was able to master Hodge theory as it then stood. He wrote a Ph.D. on it, finally presented in 1949; he had been involved in cryptographic work from about 1944, at a time of great personal difficulty, while holding an academic post in Tokyo. Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. ... In mathematics, Hodge theory is one aspect of the study of the algebraic topology of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric... Doctor of Philosophy (Ph. ... 1949 is a common year starting on Saturday. ... 1944 was a leap year starting on Saturday (link will take you to calendar). ...

In 1949 he travelled to the IAS in Princeton, 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. IAS stands for: Indicated Airspeed Ideal Adsorbed Solution - thermodynamic theory of adsorption of Minka and Myers International Accounting Standards International Adsorption Society Institute for Advanced Study Institute for Anarchist Studies The IAS computer built at the Institute for Advanced Study Institute of the Aeronautical Sciences International Association of Scientologists Indian... Hermann Weyl Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician. ... In mathematics, a sheaf F on a given topological space X gives a set or richer structure F(U) for each open set U of X. The structures F(U) are compatible with the operations of restricting the open set to smaller subsets and gluing smaller open sets to obtain... Friedrich E.P. Hirzebruch (born 17 October 1927) is a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. ...

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 of 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. Donald C. Spencer (April 25, 1912 - December 23, 2001) was an American mathematician, known for major work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of partial differential equations. ... In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions Pε, where ε is a small number, or vector of small quantities. ... In algebraic geometry, the moduli problem is to describe the parameters on which algebraic varieties depend. ... In mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. ... Alexander Grothendieck (born March 28, 1928, Berlin) is one of the greatest mathematicians of the 20th century, with major contributions to algebraic geometry, homological algebra, and functional analysis. ... In differential geometry, a G-structure on a n-manifold M, for a given structure group G (which is a Lie subgroup of the general linear group GL(n)) is a G-subbundle of the frame bundle on M. The notion of G-structures includes many other structures on manifolds...

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 P⁴, and the theorem that they form a single diffeomorphism class. Again, this work has proved foundational. In mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. ... In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ... In algebraic geometry, the function field of an irreducible algebraic variety is the field of fractions of the ring of regular functions. ... A K3 manifold is a hyperkähler manifold of real dimension 4, i. ... In mathematics, a diffeomorphism is a kind of isomorphism of smooth manifolds. ...

Kodaira left the IAS in 1961, and after two positions in the USA returned to Japan in 1967; he was professor at the University of Tokyo. He was awarded a Wolf Prize in 1984/5. He died at Kofu. The University of Tokyo (東京大学; Tōkyō Daigaku, abbreviated as 東大 Tōdai) is generally ranked as Japans most prestigious university. ... The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples, irrespective of nationality, race, colour, religion, sex or political views. The prize is awarded in Israel by the Wolf Foundation, founded by Dr. Ricardo... Kōfu, or Koufu (甲府市; -shi) is the capital city of Yamanashi, Japan. ...

See also:

• Titchmarsh-Kodaira formula
• Kodaira vanishing theorem
• Kodaira-Spencer mapping
• Kodaira dimension
• Kodaira embedding theorem

In mathematics, the pluricanonical ring of an algebraic variety V (which is non-singular), or of a complex manifold, is a graded commutative ring that is made up of the sections of powers of the canonical bundle K. More precisely, it is the graded ring R such that for n...

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