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Author:   David Mumford, QC ,  C. Musili ,  M. Nori ,  E. Previato
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   Reprint of the 1984 ed.
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   0.910kg
ISBN:  

9780817645694

ISBN 10:   0817645691
Pages:   272
Publication Date:   27 December 2006
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

An Elementary Construction of Hyperelliptic Jacobians.- Review of background in algebraic geometry.- Divisors on hyperelliptic curves.- Algebraic construction of the Jacobian of a hyperelliptic curve.- The translation-invariant vector fields.- Neumann’s dynamical system.- Tying together the analytic Jacobian and algebraic Jacobian.- Theta characteristics and the fundamental Vanishing Property.- Frobenius’ theta formula.- Thomae’s formula and moduli of hyperelliptic curves.- Characterization of hyperelliptic period matrices.- The hyperelliptic p-function.- The Korteweg-deVries dynamical system.- Fay’s Trisecant Identity for Jacobian theta functions.- The Prime Form E(x,y)..- Fay’s Trisecant Identity.- Corollaries of the identity.- Applications to solutions of differential equations.- The Generalized Jacobian of a Singular Curve and its Theta Function.- Resolution of algebraic equations by theta constants.- Resolution of algebraic equations by theta constants.

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