Lattice polytopes cut out by root systems and the Koszul property

被引：7

作者：

Payne, Sam ^{[1
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

ADVANCES IN MATHEMATICS | 2009年 / 220卷 / 03期

关键词：

Root systems; Koszul rings; Lattice polytopes; BETTI NUMBERS; TORUS ORBIT; TRIANGULATIONS; COHOMOLOGY; NORMALITY;

D O I：

10.1016/j.aim.2008.10.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：926 / 935

页数：10

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