Mapping Class Groups of Trigonal Loci

Michele Bolognesi (1) , Michael Lönne (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Mathematisches Institut [Bayreuth]

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 $\mathcal{M}ap_g$ of Riemann surfaces of genus g.

Mots clés: Moduli stacks of curves; Teichmüller spaces; Trigonal curves; Mapping class groups; Hurwitz spaces; Monodromy maps; Braid gorups; Orbifold fundamental group

Domaines: Géométrie algébrique [math.AG]

Michele Bolognesi, Michael Lönne. Mapping Class Groups of Trigonal Loci. Selecta Mathematica (New Series), 2016, 22 (1), pp.417-445. ⟨10.1007/s00029-015-0187-9⟩. ⟨hal-00973205⟩