Defining ideals of Cohen-Macaulay fiber cones

TL;DR

This paper presents a method to explicitly compute the defining ideals of Cohen-Macaulay fiber cones associated with ideals in Noetherian local rings, advancing understanding of their algebraic structure.

Contribution

It introduces a new construction for the defining ideals of Cohen-Macaulay fiber cones, providing a systematic approach to their computation.

Findings

Provides an explicit construction for defining ideals

Enhances understanding of Cohen-Macaulay fiber cones

Facilitates computation of fiber cone structures

Abstract

Let $A$ be a commutative Noetherian local ring with maximal ideal $\mathfrak{m}$, and let $I$ be an ideal. The fiber cone is then an image of the polynomial ring over the residue field $A/\mathfrak{m}$. The kernel of this map is called the defining ideal, and it is natural to ask how to compute it. In this paper, we provide a construction for the defining ideals of Cohen-Macaulay fiber cones.