A note on deformations of moduli spaces of sheaves on K3 surfaces

2011/02/09 by Arvid Perego, Perego, Arvid
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1102.1847

Abstract

In this paper we study deformation classes of moduli spaces of sheaves on a projective K3 surface. More precisely, let (S1,H1) and (S2,H2) be two polarized K3 surfaces, m∈ℕ, and for i=1,2 let mv_i be a Mukai vector on S_i such that H_i is mv_i-generic. Moreover, suppose that the moduli spaces M_mv₁(S₁,H₁) of H₁-semistable sheaves on S₁ of Mukai vector mv₁ and M_mv₂(S₂,H₂) of H₂-semistable sheaves on S₂ with Mukai vector mv₂, have the same dimension. The aim of this paper is to prove that M_mv₁(S₁,H₁) is deformation equivalent to M_mv₂(S₂,H₂), showing a conjecture of Z. Zhang contained in [18].

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