THOMPSON, A., 2013. Explicit models for threefolds fibred by K3 surfaces of degree two. Canadian Journal of Mathematics, 65(4), pp. 905-926.
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.