Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Twisted stable maps to tame Artin stacks

Authors: Dan Abramovich, Martin Olsson and Angelo Vistoli
Journal: J. Algebraic Geom. 20 (2011), 399-477
Published electronically: September 13, 2010
Erratum: J. Algebraic Geom. 24 (2015), no. 2, 399-400
MathSciNet review: 2786662
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Abstract | References | Additional Information

Abstract: We develop the theory of twisted stable maps into a tame Artin stack $ \mathcal{M}$. We show that the stacks $ \mathcal{K}_{g,n}(\mathcal{M})$ of twisted stable maps are algebraic, and proper and quasi-finite over the corresponding stacks $ \mathcal{K}_{g,n}(M)$ of stable maps of the coarse moduli space $ M$ of $ \mathcal{M}$. In the special case where $ \mathcal{M}=\mathcal{B}G$, the classifying stack of a linearly reductive group scheme $ G$, we show that $ \mathcal{K}_{g,n}(\mathcal{B}G)\to\overline{\mathcal{M}}_{g,n}$ is a flat morphism with local complete intersection fibers.

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Additional Information

Dan Abramovich
Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912

Martin Olsson
Affiliation: Department of Mathematics #3840, University of California, Berkeley, California 94720-3840

Angelo Vistoli
Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Received by editor(s): April 6, 2008
Received by editor(s) in revised form: October 4, 2009, and March 30, 2010
Published electronically: September 13, 2010
Additional Notes: The first author was supported in part by NSF grants DMS-0301695 and DMS-0603284. The second author was partially supported by NSF grant DMS-0555827 and an Alfred P. Sloan fellowship. The third author was supported in part by the PRIN Project “Geometria sulle varietà algebriche”, financed by MIUR

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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