New Derived Symmetries of some Hyperkaehler Varieties

Details New Derived Symmetries of some Hyperkaehler Varieties New Derived Symmetries of some Hyperkaehler Varieties

2011-12-02

arxiv.org/abs/1112.0487v1

Mathematics

Algebraic Geometry

52 pages

Scientific paper

We construct new autoequivalences of the derived categories of the Hilbert scheme of n points on a K3 surface and the variety of lines on a smooth cubic 4-fold. The second example and n=2 in the first use the theory of spherical functors; to deal with n>2 in the first example we develop a theory of P-functors. We conjecture that the same construction yields an autoequivalence for any moduli space of sheaves on a K3 surface. In an appendix we give a cohomology and base change criterion which is well-known to experts, but not well-documented.

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