Stacks of trigonal curves

  title={Stacks of trigonal curves},
  author={M. Bolognesi and Angelo Vistoli},
  journal={Transactions of the American Mathematical Society},
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/ g), where g is a certain algebraic group and Ug is an open subscheme of a g-equivariant vector bundle over an open subscheme of a representation of g. 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 given… Expand