Vol. 10, No. 4, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN (electronic): 2996-220X
ISSN (print): 2996-2196
Author Index
To Appear
 
Other MSP Journals
A generalization of a theorem of White

Victor Batyrev and Johannes Hofscheier

Vol. 10 (2021), No. 4, 281–296
DOI: 10.2140/moscow.2021.10.281
Abstract

An m-dimensional simplex Δ in m is called empty lattice simplex if Δ m is exactly the set of vertices of Δ. A theorem of White states that if m = 3 then, up to an affine unimodular transformation of the lattice m , any empty lattice simplex Δ 3 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.

Keywords
empty lattice simplices, Ehrhart theory, $h^*$-polynomial, Bernoulli functions, quotient singularity
Mathematical Subject Classification
Primary: 52B20
Secondary: 14B05, 11B68
Milestones
Received: 24 February 2021
Revised: 29 May 2021
Accepted: 12 June 2021
Published: 17 January 2022
Authors
Victor Batyrev
Mathematisches Institut
Universität Tübingen
Tübingen
Germany
Johannes Hofscheier
School of Mathematical Sciences
University of Nottingham
Nottingham
United Kingdom