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The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stablerank-2 sheaves on a smooth projective surface to the Uhlenbeckcompactification, and is a generalization of the Hilbert-Chow morphism forHilbert schemes of points. When the surface is the complex projective plane, wedetermine all the 1-point genus-0 Gromov-Witten invariants extremal withrespect to the Gieseker-Uhlenbeck morphism. The main idea is to understand thevirtual fundamental class of the moduli space of stable maps by studying theobstruction sheaf and using a meromorphic 2-form on the Gieseker moduli space.

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