Admissible pairs vs Gieseker-Maruyama

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 semist...

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Bibliographic Details
Published in:Sbornik. Mathematics 2019-05, Vol.210 (5), p.731-755
Main Author: Timofeeva, N. V.
Format: Article
Language:English
Subjects:
algebraic surface
moduli space
Polynomials
semistable admissible pairs
semistable coherent sheaves
Sheaves
vector bundles
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Summary: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.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM9053