On the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces

被引：0

作者：

Mata-Gutierrez, O. ^{[1
]}

Roa-Leguizamon, L. ^{[2
]}

Torres-Lopez, H. ^{[3
]}

机构：

[1] Univ Guadalajara, Ctr Univ Ciencias Exactas & Ingn, Dept Matemat, Ave Revoluc 1500, Guadalajara, Jalisco, Mexico

[2] Univ Los Andes, Dept Matemat, Carrera 1 18A-12,111 711, Bogota, Colombia

[3] Univ Autonoma Zacatecas, Conacyt UA Matemat, Calzada Solidar Entronque Paseo La Bufa, Zacatecas 98000, Zac, Mexico

来源：

GLASGOW MATHEMATICAL JOURNAL | 2023年 / 65卷 / 02期

关键词：

elementary transformation; moduli of vector bundles; moduli of sheaves; Hilbert scheme; ELEMENTARY TRANSFORMATIONS; VECTOR-BUNDLES;

D O I：

10.1017/S0017089523000010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to determine a bound of the dimension of an irreducible component of the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces. Let X be a nonsingular irreducible complex surface, and let E be a vector bundle of rank n on X. We use the m-elementary transformation of E at a point x is an element of X to show that there exists an embedding from the Grassmannian variety G(E-x, m) into the moduli space of torsion-free sheaves M-X,M-H(n; c(1), c(2) + m) which induces an injective morphism from X x M-X,M-H(n; c(1), c(2)) to Hilb(MX,H(n; c1, c2+m)).

引用

页码：414 / 429

页数：16

共 50 条

[21] The Hilbert scheme of hyperelliptic Jacobians and moduli of Picard sheaves
Ricolfi, Andrea T.
[J]. ALGEBRA & NUMBER THEORY, 2020, 14 (06) : 1381 - 1397
[22] Maximal subsheaves of torsion-free sheaves on nodal curves
Bhosle, Usha N.
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2006, 74 : 59 - 74
[23] CONTINUATION OF SECTIONS OF TORSION-FREE COHERENT ANALYTIC SHEAVES
FUJIMOTO, H
[J]. NAGOYA MATHEMATICAL JOURNAL, 1968, 31 (JAN) : 279 - &
[24] Locally torsion-free quasi-coherent sheaves
Odabasi, Sinem
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2014, 218 (09) : 1760 - 1770
[25] Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces
Minets, Alexandre
[J]. SELECTA MATHEMATICA-NEW SERIES, 2020, 26 (02):
[26] Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces
Alexandre Minets
[J]. Selecta Mathematica, 2020, 26
[27] A restriction theorem for torsion-free sheaves on some elliptic manifolds
Vuletescu, Victor
[J]. BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2013, 56 (02): : 237 - 242
[28] Stratifying families of torsion-free sheaves on a smooth surface by their singularities
Maria, V
Pitteloud, Y
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1999, 144 (03) : 277 - 296
[29] Framed torsion-free sheaves on CP2, Hilbert schemes, and representations of infinite dimensional Lie algebras
Licata, Anthony M.
[J]. ADVANCES IN MATHEMATICS, 2011, 226 (02) : 1057 - 1095
[30] GENERALIZED PARABOLIC BUNDLES AND APPLICATIONS TO TORSION-FREE SHEAVES ON NODAL CURVES
BHOSLE, U
[J]. ARKIV FOR MATEMATIK, 1992, 30 (02): : 187 - 215

← 1 2 3 4 5 →