Stacks of Trigonal Curves

  title={Stacks of Trigonal Curves},
In this paper we study the stack Tg of smooth triple covers of a conic; when g ≥ 5 this stack is embedded Mg as the locus of trigonal curves. We show that Tg is a quotient [Ug/Γg ], where Γg is a certain algebraic group and Ug is an open subscheme of a Γg-equivariant vector bundle over an open subscheme of a representation of Γg. Using this, we compute the integral Picard group of Tg when g > 1. The main tools are a result of Miranda that describes a flat finite triple cover of a scheme S as… CONTINUE READING