The Brauer group of analytic K3 surfaces
Algebraic Geometry
2007-05-23 v2 Differential Geometry
Abstract
We show that for complex analytic K3 surfaces any torsion class in H^2(X,O_X^*) comes from an Azumaya algebra. In other words, the Brauer group equals the cohomological Brauer group. For algebraic surfaces, such results go back to Grothendieck. In our situation, we use twistor spaces to deform a given analytic K3 surface to suitable projective K3 surfaces, and then stable bundles and hyperholomorphy conditions to pass back and forth between the members of the twistor family.
Cite
@article{arxiv.math/0305101,
title = {The Brauer group of analytic K3 surfaces},
author = {Daniel Huybrechts and Stefan Schroeer},
journal= {arXiv preprint arXiv:math/0305101},
year = {2007}
}
Comments
10 pages. Minor changes, to appear in Int. Math. Res. Not