Degenerations of K3 Surfaces of Degree Two
Algebraic Geometry
2013-12-09 v4
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 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.
Keywords
Cite
@article{arxiv.1010.5906,
title = {Degenerations of K3 Surfaces of Degree Two},
author = {Alan Thompson},
journal= {arXiv preprint arXiv:1010.5906},
year = {2013}
}
Comments
Final version. Accepted for publication by the Transactions of the American Mathematical Society