One dimensional cohen-macaulay rings with maximal hilbert function

Abstract

Let denote e distinct points in . Here k denotes an algebraically and is projective r-space over k. Let R denote the coordinate ring of and let A be the localization of R at its irrelevant maximal ideal. A is a reduced, Cohen-Macaulay, local ring of dimension one and multiplicity e. we suppose r ≥ 2, and for some d ≥ 2. In a previous paper, the author showed that if are in uniform position in , then the Cohen-Macaulay type, t(A), of A is given by the following formula; . The local ring A is a typical example of a ring with maximal Hilbert function. In this paper, we discuss various results for t(A), when A is one dimensional, Cohen-Macaulay, local ring with maximal Hilbert function. In particular, we obtain a natural generalization of the above mentioned geometric result.