Lattice polytopes cut out by root systems and the Koszul property
Combinatorics
2008-12-07 v2
Abstract
We show that lattice polytopes cut out by root systems of classical type are normal and Koszul, generalizing a well-known result of Bruns, Gubeladze, and Trung in type A. We prove similar results for Cayley sums of collections of polytopes whose Minkowski sums are cut out by root systems. The proofs are based on a combinatorial characterization of diagonally split toric varieties.
Keywords
Cite
@article{arxiv.0805.1252,
title = {Lattice polytopes cut out by root systems and the Koszul property},
author = {Sam Payne},
journal= {arXiv preprint arXiv:0805.1252},
year = {2008}
}
Comments
10 pages. v2: corrected treatment of G_2 case, improved exposition throughout