Work

Castelnuovo–Mumford Regularity of Unprojections and the Eisenbud–Goto Regularity Conjecture

Year: 2025

Type: article

Abstract: McCullough and Peeva found sequences of counterexamples to the Eisenbud–Goto conjecture on the Castelnuovo–Mumford regularity by using Rees-like algebras, where entries of each sequence have increasing dimensions and codimensions. In this paper we suggest another method to construct counterexamples to the conjecture with any fixed dimension $n\geq 3$ and any fixed codimension $e\geq 2$. Our strategy is an unprojection process and utilizes the possible complexity of homogeneous ideals with three generators. Furthermore, our counterexamples exhibit how singularities affect the Castelnuovo–Mumford regularity.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf017

Author: Junho Choe

Institution: Korea Institute for Advanced Study

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, National Research Foundation of Korea

OpenAlex ID: W4407122617

FWCI:

Cites: 23

Cited by: 1

Related to: 10