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arXiv · 2206.06151

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

Junho Choe
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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 $n\geq3$ and any fixed codimension $e\geq2$. 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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Junho Choe. 2022-06-13. Castelnuovo-Mumford regularity of unprojections and the Eisenbud-Goto regularity conjecture. https://arxiv.org/abs/2206.06151

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