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An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

  • Textbook
  • © 1989

Overview

Authors:
  1. Martin Schlichenmaier
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Part of the book series: Lecture Notes in Physics (LNP, volume 322)

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Table of contents (12 chapters)

  1. Front Matter

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  2. Introduction

    • Martin Schlichenmaier
    Pages V-VII

  3. Introduction from a physicist's viewpoint

    • Ian McArthur
    Pages IX-XIII

  4. Manifolds

    Pages 1-9

  5. Topology of riemann surfaces

    Pages 10-24

  6. Analytic structure

    Pages 25-36

  7. Differentials and integration

    Pages 37-47

  8. Tori and jacobians

    Pages 48-55

  9. Projective varieties

    Pages 56-66

  10. Moduli space of curves

    Pages 67-84

  11. Vector bundles, sheaves and cohomology

    Pages 85-100

  12. The theorem of riemann-roch for line bundles

    Pages 101-118

  13. The mumford isomorphism on the moduli space

    Pages 119-133

  14. Back Matter

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Keywords

About this book

This lecture is intended as an introduction to the mathematical concepts of algebraic and analytic geometry. It is addressed primarily to theoretical physicists, in particular those working in string theories. The author gives a very clear exposition of the main theorems, introducing the necessary concepts by lucid examples, and shows how to work with the methods of algebraic geometry. As an example he presents the Krichever-Novikov construction of algebras of Virasaro type. The book will be welcomed by many researchers as an overview of an important branch of mathematics, a collection of useful formulae and an excellent guide to the more extensive mathematical literature.

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