# Stacks of trigonal curves

```@article{Bolognesi2009StacksOT,
title={Stacks of trigonal curves},
author={M. Bolognesi and Angelo Vistoli},
journal={Transactions of the American Mathematical Society},
year={2009},
volume={364},
pages={3365-3393}
}```
• Published 2009
• Mathematics
• 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
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