Isomorphism of compactifications of moduli of vector bundles: nonreduced moduli

A morphism of the moduli functor of admissible semistable pairs to the Gieseker – Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface, is constructed. It is shown that these functors are isomorphic, and main components of moduli scheme for semistable admissible pairs are isomorphic to main components of the Gieseker – Maruyama moduli scheme