Moduli of stable bundles on blown up surfaces (Q1323244)

Let \(S\) be a projective smooth surface and \(\widetilde {S}\) be a blow-up of distinct points on \(S\). The author studies the relation between moduli spaces of slope-stable vector-bundles (of arbitrary rank) on \(S\) and on \(\widetilde {S}\). These moduli spaces are indeed intimately related if the polarization of \(\widetilde {S}\) (needed to define stability) is ``close'' to the pullback of the polarization of \(S\).