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Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two

Published online by Cambridge University Press:  20 November 2018

Alan Thompson*
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, e-mail:
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We consider threefolds that admit a fibration by $\text{K3}$ surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarization 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 this 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 $\text{K3}$ surfaces of degree two.

Research Article
Copyright © Canadian Mathematical Society 2013


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