1. STACKS OF TRIGONAL CURVES.
- Author
-
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 τ
g 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 wheng/ > 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 Sym3 E ⊗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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