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arXiv · 1201.0930

Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts

Antonella Grassi·Vittorio Perduca
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Abstract

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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Antonella Grassi, Vittorio Perduca. 2012-07-10. Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts. https://arxiv.org/abs/1201.0930

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