Cartwright-Sturmfels ideals associated to graphs and linear spaces
Cartwright-Sturmfels ideals associated to graphs and linear spaces
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与图和线性空间相关的 Cartwright-Sturmfels 理想
DOI：
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
E. Gorla
中科院分区：
文献类型：
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作者：
A. Conca;E. D. Negri;E. Gorla
受Cartwright和Sturmfels工作的启发，在以前的一篇论文中，我们介绍了两类以他们命名的多重分次理想。这些理想是根据它们的多级一般初始理想的性质定义的。本文的目的是证明最近引起研究者注意的三个理想族是Cartwright-Sturmfels理想。更具体地说，我们证明了二项式边理想，线性空间的多重均匀化，多视图理想是Cartwright Sturmfels理想，从而恢复和推广最近的结果Herzog-Hibi-Hreinsdottir-Kahle-Rauh，Ohtani，Ardila-Boocher，Aholt Sturmfels-托马斯，和Binglin Li。受Brion定理的启发，我们还提出了Cartwright-Sturmfels理想的局部上同调模的刚性的一个猜想。我们通过在单项式情形下证明该猜想，为该猜想提供了一些证据。
Inspired by work of Cartwright and Sturmfels, in a previous paper we introduced two classes of multigraded ideals named after them. These ideals are defined in terms of properties of their multigraded generic initial ideals. The goal of this paper is showing that three families of ideals that have recently attracted the attention of researchers are Cartwright-Sturmfels ideals. More specifically, we prove that binomial edge ideals, multigraded homogenizations of linear spaces, and multiview ideals are Cartwright-Sturmfels ideals, hence recovering and extending recent results of Herzog-Hibi-Hreinsdottir-Kahle-Rauh, Ohtani, Ardila-Boocher, Aholt-Sturmfels-Thomas, and Binglin Li. We also propose a conjecture on the rigidity of local cohomology modules of Cartwright-Sturmfels ideals, that was inspired by a theorem of Brion. We provide some evidence for the conjecture by proving it in the monomial case.
二项式边缘理想的 Castelnuovo-Mumford 正则
DOI：
10.1016/j.jcta.2015.11.004
发表时间：
2016
期刊：
J. Comb. Theory, Ser. A
影响因子：
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作者：
Saeedi Madani
通讯作者：
Saeedi Madani
影响因子：
0.8
作者：
Ardila F
通讯作者：
Ardila F