The Brauer group of analytic K3 surfaces

Details The Brauer group of analytic K3 surfaces The Brauer group of analytic K3 surfaces

2003-05-07

arxiv.org/abs/math/0305101v2

Int. Math. Res. Not. 50 (2003), 2687-2698

Mathematics

Algebraic Geometry

10 pages. Minor changes, to appear in Int. Math. Res. Not

Scientific paper

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.

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