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Cartwright-Sturmfels ideals associated to graphs and linear spaces

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Abstract

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.

Most cited references12

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Graphs and Ideals Generated by Some 2-Minors

(2011)
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Binomial edge ideals and conditional independence statements

(2010)
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ON THE GEOMETRY OF SPHERICAL VARIETIES

(2014)
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Author and article information

Journal
2017-05-01
Article
1705.00575

http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Custom metadata
22 pages
math.AC

Algebra