Tata Lectures on Theta II

  • David Mumford

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. An Elementary Construction of Hyperelliptic Jacobians

  3. Fay’s Trisecant Identity for Jacobian theta functions

    1. David Mumford
      Pages 207-213
    2. David Mumford
      Pages 214-222
    3. David Mumford
      Pages 223-238
  4. Resolution of algebraic equations by theta constants

  5. Back Matter
    Pages 271-272

About this book

Introduction

The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others.

A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to individual and mathematics research libraries.

Keywords

Divisor Identity Invariant Riemann surfaces algebra algebraic geometry equation function geometry mathematical physics mathematics

Authors and affiliations

  • David Mumford
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4578-6
  • Copyright Information Birkhäuser Boston 2007
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4569-4
  • Online ISBN 978-0-8176-4578-6
  • About this book