On the monodromy of moduli spaces of sheaves on K3 surfaces

Details On the monodromy of moduli spaces of sheaves on K3 surfaces On the monodromy of moduli spaces of sheaves on K3 surfaces

2003-05-01

arxiv.org/abs/math/0305042v3

J. Algebraic Geom. 17 (2008), 29-99.

Mathematics

Algebraic Geometry

v3: Latex, 69 pages. A major revision. Conjecture 2.6 of the previos version is proven in Theorem 1.2 of the new version. The

Scientific paper

Let S be a K3 surface and Aut D(S) the group of auto-equivalences of the derived category of S. We construct a natural representation of 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].

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