Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts

Details Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts

2012-01-04

arxiv.org/abs/1201.0930v1

Mathematics

Algebraic Geometry

Scientific paper

We study elliptically fibered K3 surfaces, with sections, in toric Fano threefolds which satisfy certain combinatorial properties. We show that some of these are equivalent to the existence of an appropriate notion of a Weierstrass model adapted to the toric context. Moreover, we show that if in addition other conditions are satisfied, there exists a semistable degeneration of the elliptic K3 surface which is compatible to the elliptic fibration and F-theory/heterotic duality.

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