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1 results

  • Derived categories of hyper-Kähler manifolds: extended Mukai vector and integral structure

  • Part of
  • Thorsten Beckmann
  • Journal:
    Compositio Mathematica / Volume 159 / Issue 1 / January 2023
    Published online by Cambridge University Press:
    31 January 2023, pp. 109-152
    Print publication:
    January 2023
    • Article
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  • We introduce a linearised form of the square root of the Todd class inside the Verbitsky component of a hyper-Kähler 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-Kähler manifolds as well as an integral lattice associated to the derived category of hyper-Kähler manifolds deformation equivalent to the Hilbert scheme of a K3 surface mimicking the surface case.