Tata Lectures on Theta II

Front Matter....Pages i-xiv
Review of background in algebraic geometry....Pages 1-11
Divisors on hyperelliptic curves....Pages 12-27
Algebraic construction of the Jacobian of a hyperelliptic curve....Pages 28-39
The translation-invariant vector fields....Pages 40-50
Neumann’s dynamical system....Pages 51-74
Tying together the analytic Jacobian and algebraic Jacobian....Pages 75-94
Theta characteristics and the fundamental Vanishing Property....Pages 95-105
Frobenius’ theta formula....Pages 106-119
Thomae’s formula and moduli of hyperelliptic curves....Pages 120-136
Characterization of hyperelliptic period matrices....Pages 137-154
The hyperelliptic p-function....Pages 155-176
The Korteweg-deVries dynamical system....Pages 177-206
The Prime Form E(x,y).....Pages 207-213
Fay’s Trisecant Identity....Pages 214-222
Corollaries of the identity....Pages 223-238
Applications to solutions of differential equations....Pages 239-242
The Generalized Jacobian of a Singular Curve and its Theta Function....Pages 243-260
Resolution of algebraic equations by theta constants....Pages 261-270
Back Matter....Pages 271-272