Document type
ArticleVersion
Published versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/224944
On the moduli space of simple sheaves on singular K3 surfaces
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
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.
Subject (English)
Citation
Citation
FANTECHI, Barbara and MIRÓ-ROIG, Rosa M. (Rosa Maria). On the moduli space of simple sheaves on singular K3 surfaces. Bulletin des Sciences Mathematiques. 2025. Vol. 199. ISSN 0007-4497. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/224944