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Table of contents (18 chapters)

Front Matter

An Elementary Construction of Hyperelliptic Jacobians

Fay’s Trisecant Identity for Jacobian theta functions

Resolution of algebraic equations by theta constants

Back Matter
About this book
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 KortewegdeVries equations as well as other nonlinear differential equations of mathematical physics.
This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a selfcontained introduction to the theory of the Jacobians. It also ties together nineteenthcentury 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
 partial differential equations
Authors and Affiliations

Division of Applied Mathematics, Brown University, Providence, USA
David Mumford
Bibliographic Information
Book Title: Tata Lectures on Theta II
Book Subtitle: Jacobian theta functions and differential equations
Authors: David Mumford
DOI: https://doi.org/10.1007/9780817645786
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2007
Softcover ISBN: 9780817645694Published: 27 December 2006
eBook ISBN: 9780817645786Published: 15 April 2012
Edition Number: 1
Number of Pages: XIV, 272
Additional Information: Originally published as volume 43 in the series: Progress in Mathematics
Topics: Special Functions, Algebraic Geometry, Mathematical Methods in Physics, Functions of a Complex Variable, Algebraic Topology, Differential Equations