Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two

Details Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two

2011-01-25

arxiv.org/abs/1101.4763v1

Mathematics

Algebraic Geometry

30 pages, 1 figure, comments welcome

Scientific paper

We consider terminal threefolds that admit a semistable fibration by K3 surfaces over a nonsingular curve, equipped with a line bundle that defines a polarisation of degree two on the general fibre. Under certain assumptions on the polarisation bundle we show that the relative log canonical model of the threefold exists and that we can explicitly reconstruct it from a small set of data that can be determined from the original fibration. Finally we prove a kind of 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 terminal threefold admitting a semistable fibration by K3 surfaces of degree two.

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