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All Weight Systems for Calabi-Yau Fourfolds from Reflexive Polyhedra

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arxiv 1808.02422 v1 pith:XUVC3VKS submitted 2018-08-07 hep-th math.AG

All Weight Systems for Calabi-Yau Fourfolds from Reflexive Polyhedra

Friedrich Sch\"oller , Harald Skarke This is my paper
classification hep-th math.AG
keywords reflexivepolytopesweightscalabi-yaufourfoldspolyhedrasystemstuples
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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For any given dimension $d$, all reflexive $d$-polytopes can be found (in principle) as subpolytopes of a number of maximal polyhedra that are defined in terms of $(d+1)$-tuples of integers (weights), or combinations of $k$-tuples of weights with $k<d+1$. We present the results of a complete classification of sextuples of weights pertaining to the construction of all reflexive polytopes in five dimensions. We find 322 383 760 930 such weight systems. 185 269 499 015 of them give rise directly to reflexive polytopes and thereby to mirror pairs of Calabi-Yau fourfolds. These lead to 532 600 483 distinct sets of Hodge numbers.

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Cited by 5 Pith papers

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