1.

Record Nr.

UNINA9910450521803321

Autore

Voisin Claire <1962->

Titolo

Hodge theory and complex algebraic geometry . 1 / / Claire Voisin ; translated by Leila Schneps [[electronic resource]]

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2002

ISBN

1-107-13070-0

1-139-63684-7

1-280-41829-X

9786610418299

1-139-14717-X

0-511-17975-8

0-511-06352-0

0-511-05719-9

0-511-30908-2

0-511-61534-5

0-511-07198-1

Descrizione fisica

1 online resource (ix, 322 pages) : digital, PDF file(s)

Collana

Cambridge studies in advanced mathematics ; ; 76

Disciplina

516.3/5

Soggetti

Hodge theory

Geometry, Algebraic

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references and indexes.

Nota di contenuto

Cover; Half-title; Series-title; Title; Copyright; Contents; 0 Introduction; Part I Preliminaries; Part II The Hodge Decomposition; Part III Variations of Hodge Structure; Part IV Cycles and Cycle Classes; Bibliography; Index

Sommario/riassunto

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.