Hodge Theory and Complex Algebraic Geometry II

by Claire Voisin , Translated by Leila Schneps

• ISBN13: 9780521718028
• ISBN10: 0521718023
• Edition: 1st
• Format: Paperback
• Copyright: 2008-02-04
• Publisher: Cambridge University Press

Summary

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. The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry. Also available: Volume I 0-521-80260-1 Hardback $60.00 C

Table of Contents

Introduction

The Topology of Algebraic Varieties

The Lefschetz theorem on hyperplane sections

Lefschetz pencils

Monodromy

The Leray spectral sequence

Variations of Hodge Structure

Transversality and applications

Hodge filtration of hypersurfaces

Normal functions and infinitesimal invariants

NoriG++s work

Algebraic Cycles

Chow groups

MumfordG++ theorem and its generalizations

The Bloch conjecture and its generalizations

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.