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

IF 0.5 4区 数学 Q3 MATHEMATICS Glasgow Mathematical Journal Pub Date : 2022-02-22 DOI:10.1017/S0017089523000010
O. Mata-Gutiérrez, L. Roa-Leguizamón, H. Torres-López
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Abstract

Abstract 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 $x \in X$ to show that there exists an embedding from the Grassmannian variety $\mathbb{G}(E_x,m)$ into the moduli space of torsion-free sheaves $\mathfrak{M}_{X,H}(n;\,c_1,c_2+m)$ which induces an injective morphism from $X \times M_{X,H}(n;\,c_1,c_2)$ to $Hilb_{\, \mathfrak{M}_{X,H}(n;\,c_1,c_2+m)}$ .
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曲面上无扭轮轴模空间的Hilbert格式
摘要本文的目的是确定表面上无扭滑轮的模量空间的Hilbert格式的不可约分量的维数的界。设X是一个非奇异的不可约复曲面,设E是X上秩为n的向量丛。我们利用E在X$中$X\点的m初等变换,证明了存在从Grassmannian变种$\mathbb{G}(E_X,m)$到无扭槽轮$\mathfrak的模空间的嵌入{M}_{X,H}(n;\,c_1,c_2+m)$,它诱导了从$X\times m_{X、H}{M}_{X,H}(n;\,c_1,c_2+m)}$。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
36
审稿时长
6-12 weeks
期刊介绍: Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics. The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.
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