1. STACKS OF TRIGONAL CURVES.
- Author
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Bolognesi, M. and Vistoli, A.
- Subjects
- *
CURVES , *ALGEBRA , *VECTOR bundles , *PICARD groups , *SHEAF theory , *LOCUS (Mathematics) , *LINEAR algebraic groups - Abstract
In this paper we study the stack τg of smooth triple covers of a conic; when g ≥ 5 this stack is embedded Mg as the locus of trigonal curves. We show that τ 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 τg when g/ > 1. τhe main tools are a result of Miranda that describes a flat finite triple cover of a scheme S as given by a locally free sheaf E of rank two on S, with a section of Sym3E ⊗detEv, and a new description of the stack of globally generated locally free sheaves of fixed rank and degree on a projective line as a quotient stack. [ABSTRACT FROM AUTHOR]
- Published
- 2012
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