Victor Batyrev
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 |
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