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

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

2009-06-15

arxiv.org/abs/0906.2688v1

Mathematics

Algebraic Geometry

20 pages. Transactions of AMS (to appear)

Scientific paper

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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