On the moduli space of simple sheaves on singular K3 surfaces

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. (c) 2024 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC license (http://creativecommons.org /licenses /by-nc /4 .0/).