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Hodge theory and complex algebraic geometry

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Published by Cambridge University Press in Cambridge, New York .
Written in English

Subjects:

  • Hodge theory.,
  • Geometry, Algebraic.

Book details:

Edition Notes

StatementClaire Voisin ; translated by Leila Schneps.
SeriesCambridge studies in advanced mathematics -- 76-77.
Classifications
LC ClassificationsQA564 .V65 2002, QA564 .V65 2002
The Physical Object
Pagination2 v. ;
ID Numbers
Open LibraryOL18215784M
ISBN 100521802601, 0521802830
LC Control Number2002017389

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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 by:   The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identit 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 /5(6).   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 . 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.

Hodge theory and complex algebraic geometry / Claire Voisin. p. cm. – (Cambridge studies in advanced mathematics) Includes bibliographical references and index. ISBN 0 1 1. Hodge theory. 2. Geometry, Algebraic. I. Title. II. Series. QAV65 5 – dc21 ISBN 0 1 hardbackCited by:   Hodge Theory and Complex Algebraic Geometry II: Volume 2 (Cambridge Studies in Advanced Mathematics Book 77) - Kindle edition by Voisin, Claire, Schneps, Leila. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Hodge Theory and Complex Algebraic Geometry II: Volume 2 5/5(1). 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. The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry.

  Buy Hodge Theory and Complex Algebraic Geometry, I: v. 1 (Cambridge Studies in Advanced Mathematics) 1 by Voisin, Claire (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.5/5(4).   The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the above/5(5). “Algebraic Geometry over the Complex Numbers” is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory. The second part of the book investigates the meaning of these results in several directions. The book is is completely self-contained and can be used by students, while its content gives an up-to-date 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.