An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

✍ Scribed by SpringerLink (Online service); Schlichenmaier, Martin

• Publisher: Springer Berlin Heidelberg
• Year: 2007
• Tongue: English
• Leaves: 227
• Series: Theoretical and Mathematical Physics;Lecture Notes in Physics
• Edition: 2nd ed. 2007
• Category: Library

✦ Synopsis

This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.

✦ Table of Contents

Preface to the Second Edition......Page 4
Preface to the First Edition......Page 8
Contents......Page 10
Introduction from a Physicist's Viewpoint......Page 13
1 Manifolds......Page 18
2 Topology of Riemann Surfaces......Page 27
3 Analytic Structure......Page 41
4 Differentials and Integration......Page 52
5 Tori and Jacobians......Page 62
6 Projective Varieties......Page 70
7 Moduli Spaces of Curves......Page 80
8 Vector Bundles, Sheaves and Cohomology......Page 96
9 The Theorem of Riemann-Roch for Line Bundles......Page 111
10 The Mumford Isomorphism on the Moduli Space......Page 127
11 Modern Algebraic Geometry......Page 141
12 Schemes......Page 163
13 Hodge Decomposition and Kahler Manifold......Page 177
14 Calabi-Yau Manifolds and Mirror Symmetry......Page 191
Appendix p-adic Numbers......Page 211
Index......Page 221