Contractions of hyper-K\"ahler fourfolds and the Brauer group
Algebraic Geometry
2022-12-12 v2
Abstract
We study the geometry of exceptional loci of birational contractions of hyper-K\"ahler fourfolds that are of K3-type. These loci are conic bundles over K3 surfaces and we determine their classes in the Brauer group. For this we use the results on twisted sheaves on K3 surfaces, on contractions and on the corresponding Heegner divisors. For a general K3 surface of fixed degree there are three (T-equivalence) classes of order two Brauer group elements. The elements in exactly two of these classes are represented by conic bundles on such fourfolds. We also discuss various examples of such conic bundles.
Keywords
Cite
@article{arxiv.2105.07697,
title = {Contractions of hyper-K\"ahler fourfolds and the Brauer group},
author = {Bert van Geemen and Grzegorz Kapustka},
journal= {arXiv preprint arXiv:2105.07697},
year = {2022}
}
Comments
to appear in Advances in Mathematics