Moduli space, Lecture 1: Automorphisms groups of Riemann surfaces, low genus examples of moduli spaces

14 Janeiro 2022, 10:00 • Davide Masoero

After introducing the moduli spaces M_{g,n} of pointed Riemann surfaces as sets, we formulate the main problem of the lectures: to put a geometry on M_{g,n}. We introduce and discuss basic properties of automorphisms groups of Riemann surfaces: we compute their dimensions for all possible values of g, and we prove that such a group is finite if g>1 (Schwarz Theorem). We discuss low genus examples of moduli spaces: M_{0,n} for n≥0, M_1, M_{1,1}.