Universal Gröbner Bases and Cartwright–Sturmfels Ideals

Abstract

Abstract The main theoretical contribution of the paper is the description of two classes of multigraded ideals named after Cartwright and Sturmfels and the study of their surprising properties. Among other things we prove that these classes of ideals have very special multigraded generic initial ideals and are closed under several operations including arbitrary multigraded hyperplane sections. As a main application we describe the universal Gröbner basis of the ideal of maximal minors and the ideal of 2-minors of a multigraded matrix of linear forms generalizing earlier results of various authors including Bernstein, Sturmfels, Zelevinsky, and Boocher.