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arXiv · 1904.01077

From Cracked Polytopes to Fano Threefolds

Thomas Prince
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Abstract

We construct Fano threefolds with very ample anti-canonical bundle and Picard rank greater than one from cracked polytopes - polytopes whose intersection with a complete fan forms a set of unimodular polytopes - using Laurent inversion; a method developed jointly with Coates-Kasprzyk. We also give constructions of rank one Fano threefolds from cracked polytopes, following work of Christophersen-Ilten and Galkin. We explore the problem of classifying polytopes cracked along a given fan in three dimensions, and classify the unimodular polytopes which can occur as 'pieces' of a cracked polytope.

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Thomas Prince. 2019-04-01. From Cracked Polytopes to Fano Threefolds. https://arxiv.org/abs/1904.01077

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