$1$-point Gromov-Witten invariants of the moduli spaces of sheaves over the projective plane
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- by Wei-Ping Li and Zhenbo Qin PDF
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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.References
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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
- MR Author ID: 334959
- Email: mawpli@ust.hk
- Zhenbo Qin
- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- Email: qinz@missouri.edu
- 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 - © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 2551-2569
- MSC (2000): Primary 14D20, 14N35
- DOI: https://doi.org/10.1090/S0002-9947-2010-05134-7
- MathSciNet review: 2763726