Universal and comprehensive Gröbner bases of the classical determinantal ideal

Let $A=(x_{ij}), i=1,2,\dots,k$, $j=1,2,\dots,l$, $1\leq k \leq l$, be a matrix of independent variables, $G$ the set of maximal minors of $A$, $I=(G)$ the classical determinantal ideal. We show that $G$ is a universal Gröbner basis of $I$. Also a sufficient condition of $G$ being a universal comprehensive Gröbner basis is proven. Bibl. – 12 titles.