Sumários
Chrash course on line bundles on compact Riemann surfaces
16 Dezembro 2021, 11:00 • Davide Masoero
Definition of line bundles
Definition of sheaves
Cohomology, short and long exact sequences
Every line bundle admits a meromorphic section
Pic(X) isomorphic to Div(X)
Lecture 9
2 Dezembro 2021, 11:00 • Davide Masoero
Completed the proof of Riemann-Roch theorem
Any genus 1 curve is isomorphic to an elliptic curve
Moduli space of genus 1 curve as the moduli space of degree 2 ramified covering of the sphere with 4 branch points
(cross-ratio, C\{0,1}/S_3 ~ C)
Lecture 8
25 Novembro 2021, 11:00 • Davide Masoero
The symmetric product of a Riemann surface, S^k X
The rank of the Abel on S^k X at a point D is equal to g(X)-i(D), where g is the genus and i(D) the speciality index of D
Riemann-Roch theorem for divisors equivalent to positive divisors
Lecture 7
18 Novembro 2021, 11:00 • Davide Masoero
Complex tori and Abelian variety
Riemann matrix and Jacobian variety
Definition of Div(X) and Cl(X) (Divisor group and divisor class group) and first properties
Abel theorem (proof) and statement of the Jacobi inverse problem