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Explicit models for threefolds fibred by K3 surfaces of degree two

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posted on 2018-10-08, 13:32 authored by Alan ThompsonAlan Thompson
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Canadian Journal of Mathematics

Volume

65

Issue

4

Pages

905 - 926

Citation

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

Publisher

© Canadian Mathematical Society

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2013

Notes

First published in Canadian Journal of Mathematics at https://doi.org/10.4153/CJM-2012-037-2. Copyright © 2013, Canadian Mathematical Society

ISSN

0008-414X

eISSN

1496-4279

Language

  • en

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