Sumários
Lecture 8
22 Abril 2020, 10:30 • Davide Masoero
Review of first 7 lectures.
The zero-curvature representation of KP and KdV
Lecture 7
15 Abril 2020, 10:30 • Davide Masoero
Solution of Jacobi's inverse problem by theta functions
The divisor class group of degree 0 is isomorphic to Jac(X) x Z
Complex structure on the symmetric product of a Riemann surface
Critical points of Abel map as special divisors
Divisors ann Riemann-Roch Theorem
1 Abril 2020, 10:30 • Davide Masoero
Definition of Divisor, principal divisors, effective divisors, degree, Divisor Class Group, Canonical Class
Classification of Divisors on the sphere
Proof of the Riemann-Roch Theorem
Consequences: genus 1 surfaces are isomorphic to an elliptic curve
Differentials and Jacobian variety
25 Março 2020, 10:30 • Davide Masoero
Definition of meromorphic and holomorphic differentials
The space of holomorphic differentials
Singular homology of a Riemann Surface
Riemann's bilinear relations
The Riemann matrix
The Abel's theorem
Explicit formulas of holomorphic differentials on the normalisation of an affine plane curve, by means of Newton's diagram techniques
Theta functions
18 Março 2020, 10:30 • Davide Masoero
Siegel upper half space
Space of theta functions of weight m, m greater or equal than 1
Theta functions with characteristics
Theta functions in dimension 1