Picard Groups of the Moduli Spaces of Riemann Surfaces with Certain Finite Abelian Symmetry Groups

Abstract: In 2021, H. Chen determined all finite abelian regular branched covers of the 2-sphere with the property that all homeomorphisms of the base preserving the branch set lift to the cover, extending the previous works of Ghaswala-Winarski and Atalan-Medettoğulları-Ozan. In this talk, we will present a consequence of this classification to the computation of Picard groups of moduli spaces of complex projective curves with certain symmetries. Indeed, we will use the work by K. Kordek already used by him for similar computations. During the talk we will try to explain the necessary concepts and tools following Kordek's work.

algebraic geometry

Audience: researchers in the discipline

ODTU-Bilkent Algebraic Geometry Seminars