The Brauer group of analytic K3 surfaces

2003/05/31 by Daniel Huybrechts, Stefan Schroeer · 1 citation
Mathematics · #math.AG #math.DG #msc:14F22 #msc:14J28 #msc:32L07 #msc:53C26

paper · pdf

published as Int. Math. Res. Not. 50 (2003), 2687-2698 · 10 pages. Minor changes, to appear in Int. Math. Res. Not

arxiv created 2003/06/10 · arxiv updated 2009/11/30

Abstract

We show that for complex analytic K3 surfaces any torsion class in H²(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.

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