2023/09/19 by Nate MacFadden, MacFadden, Nate · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Computational Physics (physics.comp-ph) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2309.10855
openalex publication_date 2023/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an algorithm for efficiently exploring inequivalent Calabi-Yau threefold hypersurfaces in toric varieties. A direct enumeration of fine, regular, star triangulations (FRSTs) of polytopes in the Kreuzer-Skarke database is foreseeably impossible due to the large count of distinct FRSTs. Moreover, such an enumeration is needlessly redundant because many such triangulations have the same restrictions to 2-faces and hence, by Wall's theorem, lead to equivalent Calabi-Yau threefolds. We show that this redundancy can be circumvented by finding a height vector in the strict interior of the intersection of the secondary cones associated with each 2-face triangulation. We demonstrate that such triangulations are generated with orders of magnitude fewer operations than the naive approach of generating all FRSTs and selecting only those differing on 2-faces. Similar methods are also presented to directly generate (the support of) the secondary subfan of all fine triangulations, relevant for random sampling of FRSTs.