The Brauer group of analytic K3 surfaces

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

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Algebraic Geometry, Differential Geometry, 14F22, 14J28, 32L07, 53C26

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http://salesiana.dossiersoluciones.com/handle/123456789/67393

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305101
 http://arxiv.org/abs/math/0305101
 Int. Math. Res. Not. 50 (2003), 2687-2698

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arXiv