English

Autoequivalences of twisted K3 surfaces

Algebraic Geometry 2019-06-05 v2

Abstract

Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures. We prove a criterion for when a given Hodge isometry arises in this way. In particular, we describe the image of the representation which associates to any autoequivalence of a twisted K3 surface its realization in cohomology: this image is a subgroup of index one or two in the group of all Hodge isometries of the twisted K3 surface. We show that both indices can occur.

Keywords

Cite

@article{arxiv.1711.00846,
  title  = {Autoequivalences of twisted K3 surfaces},
  author = {Emanuel Reinecke},
  journal= {arXiv preprint arXiv:1711.00846},
  year   = {2019}
}

Comments

25 pages; final version, to appear in Compositio Mathematica