We develop the theory of twisted stable maps into a tame Artin stack M. We show that the stacks K(g,n)(M) of twisted stable maps are algebraic, and proper and quasi-finite over the corresponding stacks K(g,n)(M) of stable maps of the coarse moduli space M of M. In the special case where M = BC, the classifying stack of a linearly reductive group scheme G, we show that K(g,n)(BG) -> (M) over bar (g,n) is a flat morphism with local complete intersection fibers.

Twisted stable maps to tame Artin stacks

VISTOLI, ANGELO
2011

Abstract

We develop the theory of twisted stable maps into a tame Artin stack M. We show that the stacks K(g,n)(M) of twisted stable maps are algebraic, and proper and quasi-finite over the corresponding stacks K(g,n)(M) of stable maps of the coarse moduli space M of M. In the special case where M = BC, the classifying stack of a linearly reductive group scheme G, we show that K(g,n)(BG) -> (M) over bar (g,n) is a flat morphism with local complete intersection fibers.
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/5729
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