Representations of Fundamental Groups of Algebraic Varieties

Kang Zuo (auth.)3540663126, 9783540663126

Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.

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Table of contents :
Introduction….Pages 1-9
Preliminaries….Pages 10-24
Harmonic metrics on flat vector bundles….Pages 25-51
Non-abelian Hodge theory, factorization theorems for non rigid or p -adic unbounded representations….Pages 52-103
Shafarevich maps for representations of fundamental groups, Kodaira dimension and Chernhyperbolicity of Shafarevich varieties….Pages 104-124