Moduli of Admissible Pairs for Arbitrary Dimension, II: Functors and Moduli

Nadezhda V. Timofeeva

Published 2020-12-26Version 1

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 a non-singular $N$-dimensional projective algebraic variety, are constructed. It is shown that these functors are isomorphic, and the moduli scheme for semistable admissible pairs $((\tilde S, \tilde L), \tilde E)$ is isomorphic to the Gieseker -- Maruyama moduli scheme. The considerations involve all components of moduli functors and corresponding moduli scheme as they exist. Bibliography: 17 items.