Workshop: Moduli of Galois covers of curves

Date: 2021-10-20

Time: 13:30 - 14:30

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Eduard Looijenga


This topic has a rich history that goes back well into the 19th century: Schwarz (1873), Picard (1880’s), Terada (1973) considered abelian covers of the projective line, culminating in the work of Deligne-Mostow (1983). The first nonabelian cases involved the icosahedral group: Wiman (1895) and later Edge (1981) considered genus 10 curve with icosahedral action (essentially completed by Farb, Dolgachev and the speaker) and Winger (1924) did the same for genus 6 curves. In this talk we go from the particular to the general: We begin with giving an almost complete story for Winger’s pencil (joint work with Yunpeng Zi). This is our stepping stone for stating a general result about the Jacobians of G-curves, of which we discuss some of its consequences and indicate its relevance for mapping class groups (joint work with Boggi).