The Abel Theorem
Speaker: Nguyen Manh Linh (École normale supérieure)

Abstract: We introduce the notions of solutions and weak solutions of a divisor on a Riemann surface, as well as those of chains, cycles, and homology. Then, we prove Abel's theorem, which gives a necessary and sufficient condition for a given divisor on a compact Riemann surface to have a meromorphic solution (i.e., to be principal). The theorem is essential to define the Jacobian variety. As an application, we reproduce the description of principal divisors on a torus.

Time: 17h30, Thursday, September 10, 2020.

Online via Zoom