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

2022/02/22 by Mata-Gutiérrez, O., Roa-Leguizamón, L., Torres-López, H.
#14D20 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.11143

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 non-singular 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 ∈ X to show that there exists an embedding from the Grassmannian variety \mathbbG(E_x,m) into the moduli space of torsion-free sheaves \mathfrakM_X,H(n;c₁,c₂+m) which induces an injective morphism from X × M_X,H(n;c₁,c₂) to Hilb_ \mathfrakM_X,H(n;c₁,c₂+m).

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