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Cambridge University Press Cambridge Hodge Theory and Complex Algebraic Geometry Vol 1

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Description

This first volume of Hodge Theory and Complex Algebraic Geometry provides a modern introduction to Kaehlerian geometry and Hodge structure. Published by Cambridge University Press as part of the Cambridge Studies in Advanced Mathematics series, this text builds a foundation starting with complex variables, complex manifolds, and holomorphic vector bundles. Readers will explore sheaves and cohomology theory, which is treated with a higher level of theoretical depth than typical geometry texts. The mathematical progression moves through the proof of Kaehler identities, leading to the hard Lefschetz theorem and the Hodge index theorem. The work culminates in the Hodge decomposition theorem, investigating the meanings of these results through several different directions. This completely self-contained volume serves as an essential resource for those studying advanced mathematics and geometry.

Key Features

This book is the first of two volumes focused on Kaehlerian geometry and Hodge structure.

The text covers fundamental topics including complex variables, complex manifolds, and holomorphic vector bundles.

It provides a theoretical treatment of sheaves and cohomology theory for advanced mathematics students.

The content leads through the Kaehler identities to the hard Lefschetz theorem and the Hodge index theorem.

This volume concludes with a detailed investigation of the Hodge decomposition theorem.

Published by Cambridge University Press as part of the Cambridge Studies in Advanced Mathematics series.

Product Specifications

Format
hardcover
Domain
Amazon UK
Release Date
05 December 2002
Listed Since
22 January 2007

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