Further Bounding the Kreuzer-Skarke Landscape
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910028719456256 |
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| author | MacFadden, Nate Orevkov, Stepan Yu. Stepniczka, Michael |
| author_facet | MacFadden, Nate Orevkov, Stepan Yu. Stepniczka, Michael |
| contents | 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 arXiv:2008.01730'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 $h^{1,1} \geq 300$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16909 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Further Bounding the Kreuzer-Skarke Landscape MacFadden, Nate Orevkov, Stepan Yu. Stepniczka, Michael High Energy Physics - Theory 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 arXiv:2008.01730'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 $h^{1,1} \geq 300$. 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. |
| title | Further Bounding the Kreuzer-Skarke Landscape |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.16909 |