# Cartwright-Sturmfels ideals associated to graphs and linear spaces

## TL;DR

This paper demonstrates that several recent important classes of ideals in algebraic geometry are Cartwright-Sturmfels ideals, extending previous results and proposing a new conjecture on their local cohomology modules.

## Contribution

It proves that binomial edge ideals, homogenizations of linear spaces, and multiview ideals are Cartwright-Sturmfels ideals, unifying and extending prior research in the field.

## Key findings

- Binomial edge ideals are Cartwright-Sturmfels ideals.
- Multigraded homogenizations of linear spaces are Cartwright-Sturmfels ideals.
- Multiview ideals are Cartwright-Sturmfels ideals.

## 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.