论文标题
Castelnuovo-Mumford的规律性不受约物和Eisenbud-Goto的规律性猜想
Castelnuovo-Mumford regularity of unprojections and the Eisenbud-Goto regularity conjecture
论文作者
论文摘要
McCullough和Peeva通过使用REES样的代数，在Castelnuovo-Mummord的规律性上找到了反述的反例 - Goto的猜想，每个序列的条目都具有增加的维度和编织性。在本文中，我们建议另一种使用任何固定尺寸$ n \ geq3 $和任何固定的codimension $ e \ geq2 $的猜想来构建反例的方法。我们的策略是一个未投入的过程，并利用了三个发电机的同质理想的可能复杂性。此外，我们的反例表现出奇异性如何影响Castelnuovo-Mumford的规律性。
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.
