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International Mathematics Research Papers (2008) Vol. 2008 : article ID rpn004, 104 pages, doi:10.1093/imrp/rpn004 published on May 9, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

A Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps

Elizabeth Baldwin1 and David Swinarski2

1 Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, UK
2 Mathematics Department, Columbia University, Room 509, MC 4406, 2990 Broadway, New York, NY 10027, USA

Correspondence: Correspondence to be sent to: baldwin{at}maths.ox.ac.uk

We construct the moduli spaces of stable maps, Formula , via geometric invariant theory (GIT). This construction is only valid over Formula , but a special case is a GIT presentation of the moduli space of stable curves of genus g with n marked points, Formula ; this is valid over Formula . In another paper by the first author, a small part of the argument is replaced, making the result valid in far greater generality. Our method follows the one used in the case n = 0 by Gieseker in [9], 1982, Lectures on Moduli of Curves to construct Formula , though our proof that the semistable set is nonempty is entirely different.


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