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Mat. Sb., 2019, Volume 210, Number 5, Pages 109–134 (Mi msb9053)  

Admissible pairs vs Gieseker-Maruyama

N. V. Timofeeva

Centre of Integrable Systems, P.G. Demidov Yaroslavl State University, Yaroslavl, Russia

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 $((\widetilde S,\widetilde L),\widetilde E)$ 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.

Keywords: moduli space, semistable coherent sheaves, semistable admissible pairs, vector bundles, algebraic surface.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.12873.2018/12.1
This work was carried out within the framework of the State Programme of the Ministry of Education and Science of the Russian Federation, project no. 1.12873.2018/12.1.


DOI: https://doi.org/10.4213/sm9053

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English version:
Sbornik: Mathematics, 2019, 210:5, 731–755

Bibliographic databases:

UDC: 512.722+512.723
MSC: 14D20
Received: 19.12.2017 and 19.07.2018

Citation: N. V. Timofeeva, “Admissible pairs vs Gieseker-Maruyama”, Mat. Sb., 210:5 (2019), 109–134; Sb. Math., 210:5 (2019), 731–755

Citation in format AMSBIB
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