Equivalences of twisted K3 surfaces

TL;DR

This paper establishes a deep connection between derived equivalences and period isomorphisms for twisted K3 surfaces, revealing structural symmetries and introducing twisted Chern characters for broader classes of varieties.

Contribution

It proves that derived equivalence implies period isomorphism for twisted K3 surfaces and characterizes the group of twisted derived equivalences via orthogonal transformations.

Findings

Derived equivalence implies isomorphic periods for twisted K3 surfaces

The converse holds for K3 surfaces with large Picard number

Twisted derived equivalences form a subgroup of the orthogonal group of cohomology

Abstract

We prove that two derived equivalent twisted K3 surfaces have isomorphic periods. The converse is shown for K3 surfaces with large Picard number. It is also shown that all possible twisted derived equivalences between arbitrary twisted K3 surfaces form a subgroup of the group of all orthogonal transformations of the cohomology of a K3 surface. The passage from twisted derived equivalences to an action on the cohomology is made possible by twisted Chern characters that will be introduced for arbitrary smooth projective varieties.