Locally trivial monodromy of moduli spaces of sheaves on K3 surfaces

In this paper we study monodromy operators on moduli spaces M v (S, H) Mᵥ (S, H) of sheaves on K3 surfaces with non-primitive Mukai vectors v v. If we write v = m w v=mw, with m > 1 m>1 and w w primitive, then our main result is that the inclusion M w (S, H) → M v (S, H) Mw (S, H) Mᵥ (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.