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Degenerations of K3 surfaces of degree two


Author: Alan Thompson
Journal: Trans. Amer. Math. Soc. 366 (2014), 219-243
MSC (2010): Primary 14D06, 14J28; Secondary 14E30
Published electronically: May 13, 2013
MathSciNet review: 3118396
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Abstract: 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 $ \mathbb{P}(1,1,1,3)$ or a complete intersection of degree $ (2,6)$ in $ \mathbb{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.


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Additional Information

Alan Thompson
Affiliation: Mathematical Institute, University of Oxford, Oxford, OX1 3LB, United Kingdom
Address at time of publication: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: amthomps@ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05759-5
Received by editor(s): January 19, 2011
Received by editor(s) in revised form: August 15, 2011, and November 9, 2011
Published electronically: May 13, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.