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

Compositio mathematica

article

Thorsten Beckmann¹ 

[1]Max-Planck-Institut für Mathematik

关键词: Hyper-Kähler manifolds;    derived categories;    moduli spaces;    Fourier–Mukai partners;    Mukai vector;    14J42;    18G80;    14J60;    14C17;   

DOI  :  10.1112/S0010437X22007849

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

CC BY