A Compactification of the Moduli Variety of Stable Vector 2-Bundles on a Surface in the Hilbert Scheme

A new compactification of the variety of moduli of stable vector 2-bundles with Chern classes $c_1$ and $c_2$ is constructed for the case in which the universal family of stable sheaves with given values of invariants is defined and there are no strictly semistable sheaves. The compactification is a subvariety in the Hilbert scheme of subschemes of a Grassmann manifold with fixed Hilbert polynomial; it is obtained from the variety of bundle moduli by adding points corresponding to locally free sheaves on surfaces which are modifications of the initial surface. Moreover, a morphism from the new compactification of the moduli space to its Gieseker–Maruyama compactification is constructed.