1009.0856 (Ugo Bruzzo et al.)

Uhlenbeck-Donaldson compactification for framed sheaves on projective
surfaces    [PDF]

Ugo Bruzzo, Dimitri Markushevich, Alexander Tikhomirov

We construct a compactification $M^{\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma \colon M^{ss} \to M^{\mu ss}$, where $M^{ss}$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.

View original: http://arxiv.org/abs/1009.0856