Locally trivial monodromy of moduli spaces of sheaves on K3 surfaces

Claudio Onorati; Arvid Perego; Antonio Rapagnetta

paper

Locally trivial monodromy of moduli spaces of sheaves on K3 surfaces

arXiv:2309.10397

Abstract

In this paper we study monodromy operators on moduli spaces $M_{v} (S, H)$ of sheaves on K3 surfaces with non-primitive Mukai vectors $v$ . If we write $v = m w$ , with $m > 1$ and $w$ primitive, then our main result is that the inclusion $M_{w} (S, H) \to M_{v} (S, H)$ as the most singular locus induces an isomorphism between the monodromy groups of these symplectic varieties, allowing us to extend to the non-primitive case a result of Markman.

52 pages, comments are very welcome!