Moduli spaces of one dimensional sheaves on log surfaces and Hilbert schemes

2025/05/01 by Takahashi, Nobuyoshi · 1 citation
#14H60 #14J42 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14B05 #Secondary 14H40

paper · doi:10.48550/arxiv.2505.00246

Abstract

Let X be a smooth projective rational surface, D⊂ X an effective anticanonical curve, β a curve class on X and \mathfrakd=∑ w_iP_i an effective divisor on D_sm. We consider the moduli space M_β(X, D, \mathfrakd) of sheaves on X which are direct images of rank-1 torsion-free sheaves on integral curves C in β such that C|_D=\mathfrakd, and show that each point of M_β(X, D, \mathfrakd) is smooth over a point in the product of the Hilbert schemes of surface singularities of types A_wi-1. Hence, M_β(X, D, \mathfrakd) has symplectic singularities and admits a unique symplectic resolution.

Citations

• The Le Bruyn-Procesi theorem following Lusztig
• Relative Log-Symplectic structure on a semi-stable degeneration of moduli of Higgs bundles
• Sheaves of maximal intersection and multiplicities of stable log maps
• Poisson structure on the moduli spaces of sheaves of pure dimension one\n on a surface
• Log BPS numbers of log Calabi-Yau surfaces
• Irreducible symplectic varieties from moduli spaces of sheaves on K3 and Abelian surfaces
• Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima\n quiver varieties
• Good degeneration of Quot-schemes and coherent systems
• Euler number of the compactified Jacobian and multiplicity of rational curves
• Desingularized moduli spaces of sheaves on a K3, II

Cited by

• Planar curve singularities relative to a smooth boundary

Related

• Some moduli spaces of 1-dimensional sheaves on an elliptic ruled surface
• Moduli spaces of framed sheaves on certain ruled surfaces over elliptic curves
• The geometry of the moduli space of one-dimensional sheaves
• On the Hilbert scheme of the moduli space of torsion free sheaves on surfaces
• On moduli spaces of sheaves on K3 or abelian surfaces