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

https://us04web.zoom.us/j/74914721760?pwd=L1VOOGEwVHZTb2htejBjUzd6aDlsdz09