For a regular ideal $I$ having a principal reduction in a Noetherian local ring $(R,\m)$ we consider properties of the powers of $I$ as reflected in the fiber cone $F(I)$ and the associated graded ring $G(I)$ of $I$. In particular, we examine the postulation number of $F(I)$ and compare it with the reduction number of $I$, and the postulation number of $G(I)$ when the latter is meaningful. We discuss a sufficient condition for $F(I)$ to be Cohen--Macaulay and consider for a fixed $R$ what is possible for the reduction number $r(I)$ of $I$ and the multiplicity of $F(I)$.
Ideals having a one-dimensional fiber cone
GUERRIERI, ANNA;
2001-01-01
Abstract
For a regular ideal $I$ having a principal reduction in a Noetherian local ring $(R,\m)$ we consider properties of the powers of $I$ as reflected in the fiber cone $F(I)$ and the associated graded ring $G(I)$ of $I$. In particular, we examine the postulation number of $F(I)$ and compare it with the reduction number of $I$, and the postulation number of $G(I)$ when the latter is meaningful. We discuss a sufficient condition for $F(I)$ to be Cohen--Macaulay and consider for a fixed $R$ what is possible for the reduction number $r(I)$ of $I$ and the multiplicity of $F(I)$.File in questo prodotto:
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