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arXiv · 2103.13382

Derived categories of hyper-K\"ahler manifolds: extended Mukai vector and integral structure

Thorsten Beckmann
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Abstract

We introduce a linearised form of the square root of the Todd class inside the Verbitsky component of a hyper-K\"ahler manifold using the extended Mukai lattice. This enables us to define a Mukai vector for certain objects in the derived category taking values inside the extended Mukai lattice which is functorial for derived equivalences. As applications, we obtain a structure theorem for derived equivalences between hyper-K\"ahler manifolds as well as an integral lattice associated to the derived category of hyper-K\"ahler manifolds deformation equivalent to the Hilbert scheme of a K3 surface mimicking the surface case.

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Thorsten Beckmann. 2021-03-24. Derived categories of hyper-K\"ahler manifolds: extended Mukai vector and integral structure. https://arxiv.org/abs/2103.13382

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