The Hodge theory of projective manifolds / Mark Andrea de Cataldo.

Format:

Book

Conference/Event

Contributor:

De Cataldo, Mark Andrea.

Conference Name:

Summer School on Hodge Theory (2003 : Byeonsan Peninsula, South Korea)

Language:

English

Subjects (All):

Manifolds (Mathematics)--Congresses.

Manifolds (Mathematics).

Topology.

Physical Description:

1 online resource (113 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press, c2007.

Language Note:

English

Summary:

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of se

Contents:

Preface; Contents; 1. Calculus on smooth manifolds; 2. The Hodge theory of a smooth, oriented, compact Riemannian manifold; 3. Complex manifolds; 4. Hermitean linear algebra; 5. The Hodge theory of Hermitean manifolds; 6. K ahler manifolds; 7. The Hard Lefschetz Theorem and the Hodge-Riemann Bilinear Relations; 8. Mixed Hodge structures, semi-simplicity and approximability; Bibliography; Index

Notes:

Eight lectures from the Summer School on Hodge Theory at the Byeonsan Peninsula in South Korea, July 22 - July 27, 2003.

Includes bibliographical references and index.

ISBN:

9786611120719

9781281120717

1281120715

9781860948657

1860948650

OCLC:

476100205