Degenerations of K3 surfaces of degree two

Thompson, Alan

doi:10.1090/S0002-9947-2013-05759-5

Degenerations of K3 surfaces of degree two
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Trans. Amer. Math. Soc. 366 (2014), 219-243 Request permission

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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