  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.
