On the moduli space of simple sheaves on singular K3 surfaces

2024/03/01 by Barbara Fantechi, Fantechi, Barbara, Rosa M. Miró‐Roig +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2403.00735

Abstract

Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \citeFM2 we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones. In this paper, we extend both Mukai's result and our construction to reduced projective K3 surfaces; for the former we need to restrict our attention to perfect sheaves. There are two key points where we cannot get a straightforward generalization. In each, we need to prove that a certain differential form on the moduli space of simple, perfect sheaves vanishes, and we introduce a smoothability condition to complete the proof.

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