A generalization of a theorem of White

Batyrev, Victor; Hofscheier, Johannes

Abstract

An m-dimensional simplex ∆ in Rm is called empty lattice simplex if ∆ ∩ Zm is exactly the set of vertices of ∆. A theorem of White states that if m = 3 then, up to an affine unimodular transformation of the lattice Zm, any empty lattice simplex ∆ ⊂ R3 is isomorphic to a tetrahedron whose vertices have third coordinate 0 or 1. We prove a generalization of this theorem for some special empty lattice simplices of arbitrary odd dimension m = 2d − 1 which was conjectured by Sebő and Borisov. Our result implies a classification of all 2d-dimensional isolated Gorenstein cyclic quotient singularities with minimal log-discrepancy ≥ d.

Citation

Batyrev, V., & Hofscheier, J. (2022). A generalization of a theorem of White. Moscow Journal of Combinatorics and Number Theory, 10(4), 281-296. https://doi.org/10.2140/moscow.2021.10.281

• Journal Article Type: Article
• Acceptance Date: Jun 12, 2021
• Online Publication Date: Dec 31, 2021
• Publication Date: Jan 17, 2022
• Deposit Date: Sep 28, 2021
• Publicly Available Date: Dec 31, 2021
• Journal: Moscow Journal of Combinatorics and Number Theory
• Print ISSN: 2220-5438
• Electronic ISSN: 2640-7361
• Publisher: Mathematical Sciences Publishers
• Peer Reviewed: Peer Reviewed
• Volume: 10
• Issue: 4
• Pages: 281-296
• DOI: https://doi.org/10.2140/moscow.2021.10.281
• Keywords: Discrete Mathematics and Combinatorics; Algebra and Number Theory
• Public URL: https://nottingham-repository.worktribe.com/output/6344106
• Publisher URL: https://msp.org/moscow/2021/10-4/moscow-v10-n4-p03-p.pdf
• Related Public URLs: https://msp.org/moscow/about/journal/about.html