Mapping class groups of trigonal loci

Michele Bolognesi ^[1] ; Michael Lönne ^[2]
1. [1] Université de Rennes 1
2. [2] Mathematisches Institut - Lehrstuhl Mathematik VII
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 1, 2016, págs. 417-445
Idioma: inglés
Enlaces
- Texto completo
Resumen
- In this paper, we study the topology of the stack TgTg of smooth trigonal curves of genus g over the complex field. We make use of a construction by the first named author and Vistoli, which describes TgTg 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 TgTg , and of its substrata with prescribed Maroni invariant, and describe their relation with the mapping class group MapgMapg of Riemann surfaces of genus g.