  The new compactification of moduli scheme of Gieseker-stable vector bundles
with the given Hilbert polynomial on a smooth projective polarized surface
(S;H), over the field k = \bar k of zero characteristic, is constructed in
previous papers of the author. Families of locally free sheaves on the surface
S are completed by the locally free sheaves on the schemes which are certain
modifications of S. We obtain the class of modified surfaces to appear in the
construction. Keywords: moduli space, semistable coherent sheaves, blowup
algebra, algebraic surface.
