# name
On the moduli space of simple sheaves on singular K3 surfaces

# metadata.dc.description.abstract[].value
Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in [6] 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.

# metadata.dc.relation.ispartof[].value
Bulletin des Sciences Mathematiques, 2025, vol. 199

# metadata.dc.rights[].value
cc by-nc (c) Fantechi, Barbara et al., 2025

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
On the moduli space of simple sheaves on singular K3 surfaces