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arXiv · 1101.4763

Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two

Alan Thompson
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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.

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Alan Thompson. 2011-01-25. Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two. https://doi.org/10.4153/cjm-2012-037-2

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