On compactifications of the space of framed vector bundles on the projective
plane -- Hans Georg Freiermuth, April 15, 2005

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I propose a new partial compactification of the space of framed vector
bundles on the projective plane with trivial determinant and second Chern
class N. Instead of adding torsion-free sheaves as in the Gieseker
compactification, the points on the new boundary are bundles on blowups of
the plane in at most N (possibly infinitely near) points which have a
prescribed splitting type along the exceptional lines.

The new space can be roughly regarded as an algebro-geometric analogue of
Taubes's bubbling compactification of the space of framed SU(r)-instantons on
S^4. It is obtained by constructing a partial desingularization of the
Uhlenbeck space regarded as an affine quotient by the method of F. Kirwan
and interpreting the objects on the exceptional divisors as vector bundles.