Journal of Algebraic Geometry

On the global quotient structure of the space of twisted stable maps to a quotient stack

Author(s): Dan Abramovich; Tom Graber; Martin Olsson; Hsian-Hua Tseng
Journal: J. Algebraic Geom. 16 (2007), 731-751.
Posted: March 7, 2007
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Abstract: Let ${\mathcal{X}}$ be a tame proper Deligne-Mumford stack of the form

where

is a scheme and

is an algebraic group. We prove that the stack ${\mathcal{K}} _{g,n}({\mathcal{X}},d)$ of twisted stable maps is a quotient stack and can be embedded into a smooth Deligne-Mumford stack. When

is finite, we give a more precise construction of ${\mathcal{K}}_{g,n}( {\mathcal{X}},d)$ using Hilbert schemes and admissible

-covers.

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Dan Abramovich
Affiliation: Department of Mathematics, Brown University, 151 Thayer Street, Providence, Rhode Island 02912
Email: abrmovic@math.brown.edu

Tom Graber
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: Department of Mathematics, California Institute of Technology, Mathematics 253-37, Caltech, Pasadena, California 91125
Email: graber@caltech.edu

Martin Olsson
Affiliation: School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540
Address at time of publication: Department of Mathematics, University of California, Berkeley, California 94720
Email: molsson@math.utexas.edu

Hsian-Hua Tseng
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C. V6T 1Z2, Canada
Email: hhtseng@math.ubc.ca

PII: S 1056-3911(07)00443-2
Received by editor(s): November 7, 2005
Received by editor(s) in revised form: November 24, 2005
Posted: March 7, 2007
Additional Notes: Research of the first author was partially supported by NSF grant DMS-0335501. Research of the second author was partially supported by NSF grant DMS-0301179 and an Alfred P. Sloan Research Fellowship. Research of the third author was partially supported by an NSF post-doctoral research fellowship.

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