We discuss the geometry of the genus one fibrations associated to an elliptic fibration on a K3 surface. We show that the two-torsion subgroup of the Brauer group of a general elliptic fibration is naturally isomorphic to the two-torsion of the Jacobian of a curve associated to the fibration. We remark that this is related to Recillas' trigonal construction. Finally we discuss the two-torsion in the Brauer group of a general K3 surface with a polarisation of degree two.

Some remarks on Brauer groups of K3 surfaces / B. van Geemen. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 197:1(2005), pp. 222-247.

Some remarks on Brauer groups of K3 surfaces

B. van Geemen
Primo
2005

Abstract

We discuss the geometry of the genus one fibrations associated to an elliptic fibration on a K3 surface. We show that the two-torsion subgroup of the Brauer group of a general elliptic fibration is naturally isomorphic to the two-torsion of the Jacobian of a curve associated to the fibration. We remark that this is related to Recillas' trigonal construction. Finally we discuss the two-torsion in the Brauer group of a general K3 surface with a polarisation of degree two.
Brauer group ; K3 surface ; elliptic fibration
Settore MAT/03 - Geometria
2005
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/6763
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