Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



On the monodromy of moduli spaces of sheaves on K3 surfaces

Author: Eyal Markman
Journal: J. Algebraic Geom. 17 (2008), 29-99
Published electronically: July 2, 2007
MathSciNet review: 2357680
Full-text PDF

Abstract | References | Additional Information

Abstract: Let $ S$ be a $ K3$ surface and $ \operatorname{Aut}D(S)$ the group of auto-equivalences of the derived category of $ S$. We construct a natural representation of $ \operatorname{Aut}D(S)$ on the cohomology of all moduli spaces of stable sheaves (with primitive Mukai vectors) on $ S$. The main result of this paper is the precise relation of this action with the monodromy of the Hilbert schemes $ S^{[n]}$ of points on the surface. A formula is provided for the monodromy representation in terms of the Chern character of the universal sheaf. Isometries of the second cohomology of $ S^{[n]}$ are lifted, via this formula, to monodromy operators of the whole cohomology ring of $ S^{[n]}$.

References [Enhancements On Off] (What's this?)

Additional Information

Eyal Markman
Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003

Received by editor(s): December 5, 2005
Published electronically: July 2, 2007
Additional Notes: The author was partially supported by NSF grant number DMS-9802532

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
AMS Website