Geodesic
Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two
Canadian journal of mathematics, Tome 65 (2013) no. 4, pp. 905-926

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DOI

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.
DOI : 10.4153/CJM-2012-037-2
Mots-clés : 14J30, 14D06, 14E30, 14J28, threefold, fibration, K3 surface 
Thompson, Alan. Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two. Canadian journal of mathematics, Tome 65 (2013) no. 4, pp. 905-926. doi: 10.4153/CJM-2012-037-2
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     title = {Explicit {Models} for {Threefolds} {Fibred} by {K3} {Surfaces} of {Degree} {Two}},
     journal = {Canadian journal of mathematics},
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     year = {2013},
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