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Bounding the Kreuzer‐Skarke Landscape
Author(s) -
Demirtas Mehmet,
McAllister Liam,
RiosTascon Andres
Publication year - 2020
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.202000086
Subject(s) - polytope , bounded function , triangulation , combinatorics , bounding overwatch , mathematics , face (sociological concept) , point set triangulation , star (game theory) , discrete mathematics , computer science , delaunay triangulation , geometry , artificial intelligence , mathematical analysis , social science , sociology
We study Calabi‐Yau threefolds with large Hodge numbers by constructing and counting triangulations of reflexive polytopes. By counting points in the associated secondary polytopes, we show that the number of fine, regular, star triangulations of polytopes in the Kreuzer‐Skarke list is bounded above by14 , 111 494 ≈ 10 928 . Adapting a result of Anclin on triangulations of lattice polygons, we obtain a bound on the number of triangulations of each 2‐face of each polytope in the list. In this way we prove that the number of topologically inequivalent Calabi‐Yau hypersurfaces arising from the Kreuzer‐Skarke list is bounded above by 10 428 . We introduce efficient algorithms for constructing representative ensembles of Calabi‐Yau hypersurfaces, including the extremal caseh 1 , 1 = 491 , and we study the distributions of topological and physical data therein. Finally, we demonstrate that neural networks can accurately predict these data once the triangulation is encoded in terms of the secondary polytope.