Castelnuovo-Mumford regularity of unprojections and the Eisenbud-Goto regularity conjecture

2022/06/13 by Choe, Junho
#14N05 (Primary) 13D02 (Secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.06151

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≥3 and any fixed codimension e≥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.

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