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18 Marzo, 2024 15:30 in punto
Sezione di Geometria, Algebra e loro applicazioni

Translation surfaces with poles and their moduli spaces

Gianluca Faraco, Università Milano Bicocca
Aula seminari III piano

On a Riemann surface $X$, every meromorphic abelian differential determines a translation surface and a representation $\chi\colon\pi_1(X)\to \mathbb C$ called period character. In this seminar we shall talk about strata of meromorphic differential with prescribed zeros and poles. Strata admit a natural foliation in which every leaf comprises translation surfaces with the same period character. In the special case of H(1,1;-2) each leaf is homeomorphic to the Loch Ness monster and it carries itself a transition structure.