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Counting Calabi-Yau Threefolds

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arxiv 2310.06820 v1 pith:S2Z6SODU submitted 2023-10-10 hep-th math.AG

Naomi Gendler , Nate MacFadden , Liam McAllister , Jakob Moritz , Richard Nally , Andreas Schachner , Mike Stillman This is my paper
classification hep-thmath.AG
keywords calabi-yauthreefoldsconnectedhypersurfacesinvariantsthreefoldalgebraicarithmetic
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abstract

We enumerate topologically-inequivalent compact Calabi-Yau threefold hypersurfaces. By computing arithmetic and algebraic invariants and the Gopakumar-Vafa invariants of curves, we prove that the number of distinct simply connected Calabi-Yau threefold hypersurfaces resulting from triangulations of four-dimensional reflexive polytopes is 4, 27, 183, 1,184 and 8,036 at $h^{1,1}$ = 1, 2, 3, 4, and 5, respectively. We also establish that there are ten equivalence classes of Wall data of non-simply connected Calabi-Yau threefolds from the Kreuzer-Skarke list. Finally, we give a provisional count of threefolds obtained by enumerating non-toric flops at $h^{1,1} =2$.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Calabi-Yau Threefolds from Vex Triangulations

    hep-th 2025-12 conditional novelty 7.0 of 10

    All fine regular triangulations of 4D reflexive polytopes—including non-FRST vex triangulations—yield smooth, birationally equivalent Calabi-Yau threefold hypersurfaces.

  2. Universality in the Axiverse

    hep-th 2025-07 conditional novelty 6.0 of 10

    Normalized divisor volumes in toric Calabi-Yau threefolds appear universal, and a GOE level-spacing model with a fitted mean reproduces axion statistics across the Kreuzer-Skarke axiverse.

  3. Coexisting Flux String Vacua from Numerical K\"ahler Moduli Stabilisation

    hep-th 2025-07 conditional novelty 5.0 of 10

    Numerical scans of Type IIB compactifications find single scalar potentials containing coexisting KKLT/LVS and Kahler-uplifted/LVS minima, including AdS, Minkowski, and dS pairs.

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