Tata Lectures on Theta II

Table of Contents

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   Book Overview
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   Chapter 1 Review of background in algebraic geometry
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   Chapter 2 Divisors on hyperelliptic curves
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   Chapter 3 Algebraic construction of the Jacobian of a hyperelliptic curve
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   Chapter 4 The translation-invariant vector fields
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   Chapter 5 Neumann’s dynamical system
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   Chapter 6 Tying together the analytic Jacobian and algebraic Jacobian
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   Chapter 7 Theta characteristics and the fundamental Vanishing Property
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   Chapter 8 Frobenius’ theta formula
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    Chapter 9 Thomae’s formula and moduli of hyperelliptic curves
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    Chapter 10 Characterization of hyperelliptic period matrices
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    Chapter 11 The hyperelliptic p-function
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    Chapter 12 The Korteweg-deVries dynamical system
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    Chapter 13 The Prime Form E(x,y).
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    Chapter 14 Fay’s Trisecant Identity
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    Chapter 15 Corollaries of the identity
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    Chapter 16 Applications to solutions of differential equations
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    Chapter 17 The Generalized Jacobian of a Singular Curve and its Theta Function
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    Chapter 18 Resolution of algebraic equations by theta constants