Universal Grobner Bases for Maximal Minors

Abstract

Bernstein, Sturmfels, and Zelevinsky proved in 1993 that the maximal minors of a matrix of variables form a universal Gröbner basis. We present a very short proof of this result, along with broad generalization to matrices with multihomogeneous structures. Our main tool is a rigidity statement for radical Borel fixed ideals in multigraded polynomial rings.