Mapping Class Groups of Trigonal Loci

Michele Bolognesi; Michael Lönne

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arXiv · 1403.7399

Mapping Class Groups of Trigonal Loci

Michele Bolognesi·Michael Lönne

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

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BibTeX RIS

Michele Bolognesi, Michael Lönne. 2014-03-28. Mapping Class Groups of Trigonal Loci. https://arxiv.org/abs/1403.7399

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