Tata Lectures on Theta II
Table of contents (18 chapters)
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Front Matter
Pages i-xiv
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An Elementary Construction of Hyperelliptic Jacobians
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Chapter
Pages 1-11
Review of background in algebraic geometry
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Chapter
Pages 12-27
Divisors on hyperelliptic curves
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Chapter
Pages 28-39
Algebraic construction of the Jacobian of a hyperelliptic curve
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Chapter
Pages 40-50
The translation-invariant vector fields
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Chapter
Pages 51-74
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Chapter
Pages 75-94
Tying together the analytic Jacobian and algebraic Jacobian
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Chapter
Pages 95-105
Theta characteristics and the fundamental Vanishing Property
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Chapter
Pages 106-119
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Chapter
Pages 120-136
Thomae’s formula and moduli of hyperelliptic curves
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Chapter
Pages 137-154
Characterization of hyperelliptic period matrices
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Chapter
Pages 155-176
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Chapter
Pages 177-206
The Korteweg-deVries dynamical system
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Fay’s Trisecant Identity for Jacobian theta functions
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Chapter
Pages 207-213
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Chapter
Pages 214-222
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Chapter
Pages 223-238
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Chapter
Pages 239-242
Applications to solutions of differential equations
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Chapter
Pages 243-260
The Generalized Jacobian of a Singular Curve and its Theta Function
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Resolution of algebraic equations by theta constants
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Chapter
Pages 261-270
Resolution of algebraic equations by theta constants
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Back Matter
Pages 271-272
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