Pawel Borówka

Title: Klein coverings of genus 2 curves

Abstract:
In the talk, we will describe the geometry of etale 4:1 coverings of genus 2 curves given by a Klein group. 
The moduli of such coverings has two connected components that are distinguished by the value of the 
Weil pairing on the group. We will show that in both cases, everything can be read from the 6 branch points 
of the curve. As a main result, we will describe the Prym variety of a covering and show that the Prym map 
is injective. This is a joint work with Angela Ortega.