Orbifold Kähler Groups related to Mapping Class groups

Abstract

We construct certain orbifold compactifications of the moduli stack of pointed stable curves over $\mathbb{C}$ and study their fundamental groups by means of their quantum representations. This enables to construct interesting Kähler groups and to settle most of the candidates for a counter-example to the Shafarevich conjecture on holomorphic convexity proposed in 1998 by Bogomolov and Katzarkov, using TQFT representations of the mapping class groups.

40p