Mapping Class Groups of Trigonal Loci

Abstract

In this paper we study the topology of the stack ${\mathcal{T}}_g$ of smooth trigonal curves of genus g, over the complex field. We make use of a construction by the first named author and Vistoli, that describes ${\mathcal{T}}_g$ as a quotient stack of the complement of the discriminant. This allows us to use techniques developed by the second named author to give presentations of the orbifold fundamental group of ${\mathcal{T}}_g$, of its substrata with prescribed Maroni invariant and describe their relation with the mapping class group $\mathcal{M}a{p}_g$ of Riemann surfaces of genus g.

To appear on Selecta Math

References in corpus (2)

• Fundamental Groups of Spaces of Smooth Projective Hypersurfaces
• Fundamental groups of moduli stacks of smooth Weierstrass fibrations