Determinantal varieties, monomial semigroups, and algebras associated with ideals

Abstract

This paper is concerned with the Rees and symmetric algebras of powers of ideals generated by A A -sequences. These algebras are represented as quotients of polynomial rings over A A by ideals defined by minors of matrices. Their Krull dimensions are computed when A A is a finite domain over a field. When A A is a polynomial ring over a Cohen-Macaulay ring A 0 {A_0} and the A A -sequence consists of indeterminates, the Rees algebra is shown to be Cohen-Macaulay. If furthermore A 0 {A_0} is a finite domain over a field, the symmetric algebra is shown to be Cohen-Macaulay only for A A -sequences and squares of A A -sequences of length two. Connections with algebras generated by monomials and Veronese varieties are pointed out.