Degenerations of K3 Surfaces of Degree Two
arXiv:1010.5906 · doi:10.1090/S0002-9947-2013-05759-5
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.
Final version. Accepted for publication by the Transactions of the American Mathematical Society