90 research outputs found
Some remarks on Brauer groups of K3 surfaces
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.Comment: This replacement has a more general theorem (thm 6.2) on Brauer
groups of double covers of rational surfaces. Corrected some typos, updated
references. To appear in Advances in Mathematic
Nikulin involutions on K3 surfaces
We study the maps induced on cohomology by a Nikulin (i.e. a symplectic)
involution on a K3 surface. We parametrize the eleven dimensional irreducible
components of the moduli space of algebraic K3 surfaces with a Nikulin
involution and we give examples of the general K3 surface in various
components. We conclude with some remarks on Morrison-Nikulin involutions,
these are Nikulin involutions which interchange two copies of E_8(-1) in the
Neron Severi group.Comment: 24 page
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