Year: 2026
Type: article
Abstract: A bstract Batyrev’s construction provides a map from fine, regular, star triangulations (FRSTs) of 4D reflexive polytopes to smooth Calabi-Yau threefolds (CYs). We prove that there are at most 10 296 diffeomorphism classes of CYs produced in this manner, improving ref. [1]’s upper bound of 10 428 . To show this, we make use of the fact that any two FRSTs with the same 2-face restrictions give rise to diffeomorphic CYs and bound the number of such ‘2-face equivalence classes’ for all polytopes with Hodge number h 1,1 ≥ 300. We also put a lower bound of 10 276 on the number of 2-face equivalence classes, but emphasize that this is not a lower bound on the number of diffeomorphism classes of CYs, as distinct 2-face equivalence classes may give rise to diffeomorphic threefolds.
Source: Journal of High Energy Physics
Institutions: Cornell University, Université de Toulouse
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
Award: Theoretical Particle Physics
OpenAlex ID: W7130716038