Equidimensional symmetric algebras and residual intersections

Abstract

For a finitely generated module $M$, over a universally catenary local ring, whose symmetric algebra is equidimensional, the ideals generated by the rows of a minimal presentation matrix are shown to have height at most $\mu(M) - \rank M$. Moreover, in the extremal case, they are Cohen-Macaulay ideals if the symmetric algebra is Cohen-Macaulay. Some applications are given to residual intersections of ideals.