Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two
arXiv:1101.4763 · doi:10.4153/CJM-2012-037-2
Abstract
We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally we prove a converse to the above statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.
Early sections have been restructured and shortened. Assumptions required for the main construction have been weakened. Final version, accepted for publication by the Canadian Journal of Mathematics