Generalized binomial edge ideals are Cartwright-Sturmfels
Appears in collection : The Ubiquity of Commutative Algebra / Ubiquité de l'algèbre commutative
Let X be an m × n matrix of indeterminates and let G = ([n], E) be a graph. The generalized binomial edge ideal associated to G is the ideal I_G generated by the 2-minors of X obtained by choosing two arbitrary rows and two columns j, k such that { j,k}$ \in E$ In earlier joint work with A. Conca and E. Gorla, it was shown that I_G is Cartwright–Sturmfels in the case G = K_n and for arbitrary graphs G when m = 2. We prove that the Cartwright–Sturmfels property holds for all m and all graphs G, by establishing general results on ideal constructions that preserve this property. We also provide classes ofexamples and counterexamples for higher size minors. This is joint work with A. Conca and V. Welker.
