Databases of quantum periods for Fano manifolds

Coates, Tom; Kasprzyk, Alexander M.

Abstract

Fano manifolds are basic building blocks in geometry - they are, in a precise sense, atomic pieces of shapes. The classification of Fano manifolds is therefore an important problem in geometry, which has been open since the 1930s. One can think of this as building a Periodic Table for shapes. A recent breakthrough in Fano classification involves a technique from theoretical physics called Mirror Symmetry. From this perspective, a Fano manifold is encoded by a sequence of integers: the coefficients of a power series called the regularized quantum period. Progress to date has been hindered by the fact that quantum periods require specialist expertise to compute, and descriptions of known Fano manifolds and their regularized quantum periods are incomplete and scattered in the literature. We describe databases of regularized quantum periods for Fano manifolds in dimensions up to four. The databases in dimensions one, two, and three are complete; the database in dimension four will be updated as new four-dimensional Fano manifolds are discovered and new regularized quantum periods computed.

Citation

Coates, T., & Kasprzyk, A. M. (2022). Databases of quantum periods for Fano manifolds. Scientific Data, 9, Article 163. https://doi.org/10.1038/s41597-022-01232-6

• Journal Article Type: Article
• Acceptance Date: Feb 7, 2022
• Online Publication Date: Apr 12, 2022
• Publication Date: Dec 1, 2022
• Deposit Date: Feb 15, 2022
• Publicly Available Date: Apr 12, 2022
• Journal: Scientific Data
• Electronic ISSN: 2052-4463
• Publisher: Nature Publishing Group
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Article Number: 163
• DOI: https://doi.org/10.1038/s41597-022-01232-6
• Keywords: Library and Information Sciences; Statistics, Probability and Uncertainty; Computer Science Applications; Education; Information Systems; Statistics and Probability
• Public URL: https://nottingham-repository.worktribe.com/output/7468380
• Publisher URL: https://www.nature.com/articles/s41597-022-01232-6