Hodge Theory and Complex Algebraic Geometry I (Paperback)

Claire Voisin

ISBN 10: 0521718015 / ISBN 13: 9780521718011

Published by Cambridge University Press, Cambridge, 2008

About this Item

Paperback. The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780521718011

Bibliographic Details

• Title: Hodge Theory and Complex Algebraic Geometry I (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2008
• Language: English
• ISBN 10: 0521718015
• ISBN 13: 9780521718011
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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.

About the Author

Claire Voisin is a Professor at the Institut des Hautes Études Scientifiques, France