Lattice polytopes cut out by root systems and the Koszul property

Details Lattice polytopes cut out by root systems and the Koszul property Lattice polytopes cut out by root systems and the Koszul property

2008-05-08

arxiv.org/abs/0805.1252v2

Adv. Math. 220 (2009), 926--935.

Mathematics

Combinatorics

10 pages. v2: corrected treatment of G_2 case, improved exposition throughout

Scientific paper

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.

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