Tata Lectures on Theta II

Authors:

ISBN: 978-0-8176-4569-4 (Print) 978-0-8176-4578-6 (Online)

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiv

  2. An Elementary Construction of Hyperelliptic Jacobians

    1. No Access

      Book Chapter

      Pages 1-11

      Review of background in algebraic geometry

    2. No Access

      Book Chapter

      Pages 12-27

      Divisors on hyperelliptic curves

    3. No Access

      Book Chapter

      Pages 28-39

      Algebraic construction of the Jacobian of a hyperelliptic curve

    4. No Access

      Book Chapter

      Pages 40-50

      The translation-invariant vector fields

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      Book Chapter

      Pages 51-74

      Neumann’s dynamical system

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      Book Chapter

      Pages 75-94

      Tying together the analytic Jacobian and algebraic Jacobian

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      Book Chapter

      Pages 95-105

      Theta characteristics and the fundamental Vanishing Property

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      Book Chapter

      Pages 106-119

      Frobenius’ theta formula

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      Book Chapter

      Pages 120-136

      Thomae’s formula and moduli of hyperelliptic curves

    10. No Access

      Book Chapter

      Pages 137-154

      Characterization of hyperelliptic period matrices

    11. No Access

      Book Chapter

      Pages 155-176

      The hyperelliptic p-function

    12. No Access

      Book Chapter

      Pages 177-206

      The Korteweg-deVries dynamical system

  3. Fay’s Trisecant Identity for Jacobian theta functions

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      Book Chapter

      Pages 207-213

      The Prime Form E(x,y).

    2. No Access

      Book Chapter

      Pages 214-222

      Fay’s Trisecant Identity

    3. No Access

      Book Chapter

      Pages 223-238

      Corollaries of the identity

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      Book Chapter

      Pages 239-242

      Applications to solutions of differential equations

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      Book Chapter

      Pages 243-260

      The Generalized Jacobian of a Singular Curve and its Theta Function

  4. Resolution of algebraic equations by theta constants

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      Book Chapter

      Pages 261-270

      Resolution of algebraic equations by theta constants

  5. Back Matter

    Pages 271-272