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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ 1$-point Gromov-Witten invariants of the moduli spaces of sheaves over the projective plane


Authors: Wei-Ping Li and Zhenbo Qin
Journal: Trans. Amer. Math. Soc. 363 (2011), 2551-2569
MSC (2000): Primary 14D20, 14N35
Published electronically: December 15, 2010
MathSciNet review: 2763726
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Abstract: The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-$ 2$ sheaves on a smooth projective surface to the Uhlenbeck compactification and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points. When the surface is the complex projective plane, we determine all the $ 1$-point genus-0 Gromov-Witten invariants extremal with respect to the Gieseker-Uhlenbeck morphism. The main idea is to understand the virtual fundamental class of the moduli space of stable maps by studying the obstruction sheaf and using a meromorphic $ 2$-form on the Gieseker moduli space.


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Additional Information

Wei-Ping Li
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Email: mawpli@ust.hk

Zhenbo Qin
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: qinz@missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05134-7
PII: S 0002-9947(2010)05134-7
Keywords: Gieseker moduli spaces, Gromov-Witten invariants.
Received by editor(s): February 6, 2009
Received by editor(s) in revised form: June 1, 2009
Published electronically: December 15, 2010
Additional Notes: The first author was partially supported by the grants GRF601905 and GRF601808
The second author was partially supported by an NSF grant
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.