In this paper we study monodromy operators on moduli spaces Mv(S, H) of sheaves on K3 surfaces with non-primitive Mukai vectors v. If we write v = mw, with m > 1 and w primitive, then our main result is that the inclusion 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.
Locally trivial monodromy of moduli spaces of sheaves on K3 surfaces
Claudio Onorati;Arvid Perego;
2024-01-01
Abstract
In this paper we study monodromy operators on moduli spaces Mv(S, H) of sheaves on K3 surfaces with non-primitive Mukai vectors v. If we write v = mw, with m > 1 and w primitive, then our main result is that the inclusion 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.
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