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Degenerations of K3 surfaces of degree two

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posted on 08.10.2018, 13:16 by Alan ThompsonAlan Thompson
We consider a semistable degeneration of K3 surfaces, equipped with an effective divisor that defines a polarisation of degree two on a general fibre. We show that the map to the relative log canonical model of the degeneration maps every fibre to either a sextic hypersurface in P(1, 1, 1, 3) or a complete intersection of degree (2, 6) in P(1, 1, 1, 2, 3). Furthermore, we find an explicit description of the hypersurfaces and complete intersections that can arise, thereby giving a full classification of the possible singular fibres.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Transactions of the American Mathematical Society

Volume

366

Issue

1

Pages

219 - 243

Citation

THOMPSON, A., 2014. Degenerations of K3 surfaces of degree two. Transactions of the American Mathematical Society, 366(1), pp. 219-243.

Publisher

© American 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

2014

Notes

First published in Transactions of the American Mathematical Society, 366(1), pp. 219-243 2014, published by the American Mathematical Society.

ISSN

0002-9947

eISSN

1088-6850

Language

en

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