On a morphism of compactifications of moduli scheme of vector bundles

A morphism of nonreduced Gieseker–Maruyama functor (of semistable coherent torsion-free sheaves) on the surface to the nonreduced functor of admissible semistable pairs with the same Hilbert polynomial, is constructed. This leads to the morphism of moduli schemes with possibly nonreduced scheme structures. As usually, we study subfunctors corresponding to main components of moduli schemes.