Derived categories of hyper-Kähler manifolds via the extended Mukai lattice

Abstract: The derived category of a K3 surface is governed by its integral cohomology together with its Hodge structure and to objects we can functorially assign a Mukai vector in this lattice. We show an analogous picture for higher-dimensional hyper-Kähler manifolds using the extended Mukai lattice. In particular, we construct a vector for certain objects in the derived category taking values in the extended Mukai lattice and we obtain a rank 25 integral lattice with a Hodge structure which is a derived invariant for hyper-Kähler manifolds deformation-equivalent to the Hilbert scheme of n points on a K3 surface.

algebraic geometry

Audience: researchers in the topic

Derived seminar

Series comments: https://ed-ac-uk.zoom.us/j/89993982042

Password: a simply-connected two-dimensional variety with trivial canonical bundle (omit the space)