Riemann Surfaces

Prof. Roberto Mossa
University of Cagliari, Italy

Abstract

This 16-hour PhD course is devoted to algebraic functions on Riemann surfaces, following Forster’s Lectures on Riemann Surfaces up to §8 (Algebraic Functions), with emphasis on the construction of the associated Riemann surfaces and on Puiseux expansions near branch points.

In the final part we will explain how these classical tools naturally appear in recent problems in Kähler geometry, notably in the study of Nash–algebraic functions, simultaneous normalization, and rigidity of holomorphic isometries into Kähler manifolds. As a case study we will discuss the paper A. Loi, R. Mossa, Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds, Proc. Amer. Math. Soc. 152 (2024), no. 7.

Schedule

The course will take place in January-February 2026. The course consists of 16 hours divided into 8 lectures. The exact schedule will be announced soon.

Exam

The final exam consists in a seminar on a topic building on the content of the course. The topic for the final exam may be proposed by the students themselves or chosen from a list provided at the end of the lectures.