S. Cutkosky

activity

19982026

most citedLocal factorization and monomialization of morphisms

41 citations · 172 across the 60 of their papers we have counts for

collaborators

77 papers

math.AC2026

Limits of Amao multiplicities and Epsilon multiplicity

Steven Dale Cutkosky

Let $R$ be a $d$ -dimensional Noetherian local ring with maximal ideal $m_{R}$ and let $I$ be an ideal of $R$ . The epsilon multiplicity $ε (I)$ of $I$ is defined by Ulrich and Validash…

math.AC2026

Multiplicities of graded families of ideals on Noetherian local rings

Steven Dale Cutkosky

Let $R$ be a $d$ -dimensional Noetherian local ring with maximal ideal $m_{R}$ . In this article, we give a generalization of the multiplicity $e (I)$ of an $m_{R}$ -primary ideal $I$ of $…

math.AC2025

The Proj of the Rees algebra of a graded family of ideals

Steven Dale Cutkosky

In this article we investigate the condition that the Proj of a Rees algebra of a graded family of ideals in a Noetherian local ring $R$ is Noetherian. In many cases, the Proj will…

math.AC2025

Degree functions of graded families of ideals

Steven Dale Cutkosky, Jonathan Montaño

We express multiplicities and degree functions of graded families of $m_{R}$ -primary ideals in an excellent normal local ring $(R, m_{R})$ as limits of intersectio…

math.AC2025

Multiplicities and degree functions in local rings via intersection products

Steven Dale Cutkosky, Jonathan Montaño

We prove a theorem on the intersection theory over a Noetherian local ring $R$ , which gives a new proof of a classical theorem of Rees about degree functions. To obtain this, we de…

math.AC2024

Rees Algebras and the reduced fiber cone of divisorial filtrations on two dimensional normal local rings

Steven Dale Cutkosky

Let $I = {I_{n}}$ be a divisorial filtration on a two dimensional normal excellent local ring $(R, m_{R})$ . Let $R [I] = \oplus_{n \geq 0} I_{n}$ be the Rees algebra of $\math…