Lattice polytopes cut out by root systems and the Koszul property
Lattice polytopes cut out by root systems and the Koszul property
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根系切出的晶格多面体和科祖尔性质
DOI：
10.1016/j.aim.2008.10.008
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发表时间：
2008
影响因子：
1.7
通讯作者：
S. Payne
中科院分区：
文献类型：
--
作者：
S. Payne
我们证明了由经典型根系切出的格多面体是正规的和Koszul的，推广了Bruns，Gubeladze和Trung在A型中的一个著名结果。我们证明了类似的结果凯莱和集合的多面体的闵可夫斯基和切断根系。证明是基于对角分裂环面品种的组合特征。
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.