README.md

MLcCY7

Repository for generation of Calabi-Yau links from wp4 spaces, computation of their topological properties (Sasakian Hodge numbers, CN invariant), and their ML.

The Data folder lists the 7555 weights which create wp4 spaces which admit CY3 hypersurfaces in file WP4s.txt (the respective CY Hodge numbers $(h^{1,1},h^{2,1})$ are listed in WP4_Hodges.txt). CY polynomials (with the required singularity structure to create a CY link) are given in CYPolynomials.txt, as well as the respective topological invariant data in the file Topological_Data.txt listing each weight system, CY polynomial, Sasakian Hodge numbers, CN invariant, then Groebner basis length respectively. A selection of Groebner bases are given explicitly in the zipped file also.

The CY3PolynomialGeneration.sage script details how the CY3s where generated, ensuring the correct singularity structure. The CYLinkInvariantComputation.sage script details how the respective topological invariants were computed (code is parallelised for efficiency). The wREquivalenceChecks.sage script contains general functionality for statistically verifying the weak R-Equivalence conjecture across the database.

The remaining scripts perform the respective ML investigations as detailed in the paper.

BibTeX Citation

@article{Aggarwal:2023swe,
    author = "Aggarwal, Daattavya and He, Yang-Hui and Heyes, Elli and Hirst, Edward and Earp, Henrique N. S\'a and Silva, Tom\'as S. R.",
    title = "{Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds}",
    eprint = "2310.03064",
    archivePrefix = "arXiv",
    primaryClass = "math.DG",
    reportNumber = "QMUL-PH-23-14",
    doi = "10.1016/j.physletb.2024.138517",
    journal = "Phys. Lett. B",
    volume = "850",
    pages = "138517",
    year = "2024"
}