Fantechi, BarbaraMiró-Roig, Rosa M. (Rosa Maria)2025-12-152025-12-152025-03-010007-4497https://hdl.handle.net/2445/224944Mukai 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.24 p.application/pdfengcc by-nc (c) Fantechi, Barbara et al., 2025http://creativecommons.org/licenses/by-nc/4.0/Superfícies algebraiquesTeoria dels feixosAlgebraic surfacesSheaf theoryinfo:eu-repo/semantics/article7540192025-12-15info:eu-repo/semantics/openAccess