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 $F(I)$.
9780824705534
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/38597
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