Abstract
Morphisms between the moduli functor of admissible semistable pairs and the Gieseker-Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface are constructed. It is shown that these functors are isomorphic, and the moduli scheme for semistable admissible pairs is isomorphic to the Gieseker-Maruyama moduli scheme. All the components of moduli functors and corresponding moduli schemes which exist are looked at here. Bibliography: 16 titles.
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