An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts

Abstract

Even a cursory inspection of the Hodge plot associated with Calabi-Yau threefolds that are hypersurfaces in toric varieties reveals striking structures. These patterns correspond to webs of elliptic-K3 fibrations whose mirror images are also elliptic-K3 fibrations. Such manifolds arise from reflexive polytopes that can be cut into two parts along slices corresponding to the K3 fibers. Any two half-polytopes over a given slice can be combined into a reflexive polytope. This fact, together with a remarkable relation on the additivity of Hodge numbers, explains much of the structure of the observed patterns.

30 pages, 15 colour figures

References in corpus (1)

• On the Hodge structure of elliptically fibered Calabi-Yau threefolds

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