  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.
