Gabriele Balletti
On the maximum dual volume of a canonical Fano polytope
Balletti, Gabriele; Kasprzyk, Alexander M.; Nill, Benjamin
Abstract
We give an upper bound on the volume vol(P*) of a polytope P* dual to a d-dimensional lattice polytope P with exactly one interior lattice point, in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp, and is achieved by the dual to a particular reflexive simplex. Our result implies a sharp upper bound on the volume of a d-dimensional reflexive polytope. Translated into toric geometry, this gives a sharp upper bound on the anti-canonical degree $(-K_X)^d$ of a d-dimensional toric Fano variety X with at worst canonical singularities.
Citation
Balletti, G., Kasprzyk, A. M., & Nill, B. (2022). On the maximum dual volume of a canonical Fano polytope. Forum of Mathematics, Sigma, 10, Article e109. https://doi.org/10.1017/fms.2022.93
Journal Article Type | Article |
---|---|
Acceptance Date | Jun 26, 2022 |
Online Publication Date | Dec 13, 2022 |
Publication Date | Dec 13, 2022 |
Deposit Date | Sep 11, 2022 |
Publicly Available Date | Dec 13, 2022 |
Journal | Forum of Mathematics, Sigma |
Print ISSN | 2050-5094 |
Electronic ISSN | 2050-5094 |
Publisher | Cambridge University Press |
Peer Reviewed | Peer Reviewed |
Volume | 10 |
Article Number | e109 |
DOI | https://doi.org/10.1017/fms.2022.93 |
Keywords | Computational Mathematics; Discrete Mathematics and Combinatorics; Geometry and Topology; Mathematical Physics; Statistics and Probability; Algebra and Number Theory; Theoretical Computer Science; Analysis |
Public URL | https://nottingham-repository.worktribe.com/output/2461955 |
Publisher URL | https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/on-the-maximum-dual-volume-of-a-canonical-fano-polytope/36121F80310E40113B38A45B164C4967 |
Additional Information | Copyright: © The Author(s), 2022. Published by Cambridge University Press; License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.; Free to read: This content has been made available to all. |
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