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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Further bounding the Kreuzer-Skarke landscape

  • Nate MacFadden1
  • Stepan Yu. Orevkov2
  • Michael Stepniczka1
  1. 1Cornell University
  2. 2Université de Toulouse
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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.

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Cite

BibTeXRIS
BibTeX
@article{macfadden2026further,
  title = {{Further bounding the Kreuzer-Skarke landscape}},
  author = {Nate MacFadden and Stepan Yu. Orevkov and Michael Stepniczka},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)062},
  url = {https://link.springer.com/10.1007/JHEP10(2026)062},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Further bounding the Kreuzer-Skarke landscape
AU  - Nate MacFadden
AU  - Stepan Yu. Orevkov
AU  - Michael Stepniczka
PY  - 2026
DA  - 2026/10/07
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)062
UR  - https://link.springer.com/10.1007/JHEP10(2026)062
AB  - 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.
SN  - 1029-8479
ER  -