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arxiv: 1201.0930 · v3 · pith:RYHEEKTRnew · submitted 2012-01-04 · 🧮 math.AG · hep-th

Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts

classification 🧮 math.AG hep-th
keywords toricellipticconditionsdualityf-theoryheteroticweierstrassadapted
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We study elliptically fibered K3 surfaces, with sections, in toric Fano threefolds which satisfy certain combinatorial properties relevant to F-theory/Heterotic duality. We show that some of these conditions 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 toric semistable degeneration of the elliptic K3 surface which is compatible with the elliptic fibration and F-theory/Heterotic duality.

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