Hodge Theory and Complex Algebraic Geometry I
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Description: This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $62.00
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 12/20/2007
Size: 6.00" wide x 8.75" long x 0.75" tall
Claire Voisin has been a senior researcher at France's National Center for Scientific Research since 1986.
|Holomorphic functions of many variables|
|Sheaves and cohomology|
|The Hodge Decomposition|
|Harmonic forms and cohomology|
|The case of K+ï¿½hler manifolds|
|Hodge structures and polarisations|
|Holomorphic de Rham complexes|
|Variations of Hodge Structure|
|Families and deformations|
|Variations of Hodge structure|
|Cycles and Cycle Classes|
|The AbelG++Jacobi map|