DEGENERATIONS OF K3 SURFACES OF DEGREE TWO

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.