Degenerations of K3 Surfaces of Degree Two

Details Degenerations of K3 Surfaces of Degree Two Degenerations of K3 Surfaces of Degree Two

2010-10-28

arxiv.org/abs/1010.5906v4

Mathematics

Algebraic Geometry

Final version. Accepted for publication by the Transactions of the American Mathematical Society

Scientific paper

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.

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