Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts

2012/01/04 by Antonella Grassi, Grassi, Antonella, Vittorio Perduca +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.AG

paper · pdf · doi:10.48550/arxiv.1201.0930

References added

arxiv created 2012/07/10 · arxiv updated 2012/07/11

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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