Riemann Surfaces and Algebraic Curves

Riemann Surfaces and Algebraic Curves - WS 2020/21

Instructors : Daniele Agostini and Rainer Sinn.

Office hours: By appointment.

Lectures: Wednesday 15:15 - 16:45.

Exercise Sessions: Wednesday, 11:00 - 12:30.

Virtual meeting: The course will take place on Zoom. Please send an email to Daniele Agostini to get the videobroadcast link.

Important announcements

Course description

The course will be a first introduction to Riemann surfaces and algebraic curves. These are beautiful objects which sit at the intersection of algebra, geometry and analysis. Indeed, on one side these are complex manifolds of dimension one, and on the other they are varieties defined as a zero locus of polynomial equations. Furthermore, they are ubiquitous throughout mathematics, from diophantine equations in number theory to water waves in mathematical physics and Teichmüller theory in dynamical systems.

We will aim to cover the theorems of Riemann-Hurwitz and Riemann-Roch, meromorphic functions and their zeroes and poles, plane curves and elliptic curves, abelian integrals, the theorem of Abel-Jacobi and the construction of Jacobian varieties. Time permitting, we might touch upon further topics such as canonical curves, moduli spaces, the Schottky problem and tropical curves.

Prerequisites: abstract algebra and familiarity with differential or algebraic geometry.

References : Notes for some of the lectures will appear below. We will not follow exactly any particular book, but the main inspirations for the course will be

There are many other beautiful references for this topic. Some of them are:

Course log

A brief description of each lecture's content, together with some notes, will appear here.

Exercise sheets

The exercises will appear below and will be discussed together in the session of Wednesday morning at the MPI-MiS.
Last modified: Mon Apr 12 21:14:14 CEST 2021