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

Li, Wei-Ping; Qin, Zhenbo

doi:10.1090/S0002-9947-2010-05134-7

$1$-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

Trans. Amer. Math. Soc. 363 (2011), 2551-2569 Request permission

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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