On reduction numbers and Castelnuovo–Mumford regularity of blowup rings and modules

IF 0.7 2区 数学 Q2 MATHEMATICS
Cleto B. Miranda-Neto, Douglas S. Queiroz
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引用次数: 0

Abstract

We prove new results on the interplay between reduction numbers and the Castelnuovo–Mumford regularity of blowup algebras and blowup modules, the key basic tool being the operation of Ratliff–Rush closure. First, we answer in two particular cases a question of M. E. Rossi, D. T. Trung, and N. V. Trung about Rees algebras of ideals in two-dimensional Buchsbaum local rings, and we even ask whether one of such situations always holds. In another theorem we largely generalize a result of A. Mafi on ideals in two-dimensional Cohen–Macaulay local rings, by extending it to arbitrary dimension (and allowing for the setting relative to a Cohen–Macaulay module). We derive a number of applications, including a characterization of (polynomial) ideals of linear type, progress on the theory of generalized Ulrich ideals, and improvements of results by other authors.

关于炸环和模块的还原数和卡斯特诺沃-蒙福德正则性
我们证明了炸子代数和炸子模块的还原数与卡斯特努沃-蒙福德正则性之间相互作用的新结果,其中关键的基本工具是拉特利夫-拉什闭包操作。首先,我们在两种特殊情况下回答了 M. E. Rossi、D. T. Trung 和 N. V. Trung 提出的关于二维布赫斯鲍姆局部环中理想的里斯代数的问题,我们甚至提出了这样的情况之一是否总是成立的问题。在另一个定理中,我们在很大程度上概括了马菲(A. Mafi)关于二维科恩-麦考莱局部环中理想的一个结果,将其扩展到任意维度(并允许相对于科恩-麦考莱模块的设定)。我们推导了一些应用,包括线性类型(多项式)理想的表征、广义乌尔里希理想理论的进展以及其他作者成果的改进。
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来源期刊
Collectanea Mathematica
Collectanea Mathematica 数学-数学
CiteScore
2.70
自引率
9.10%
发文量
36
审稿时长
>12 weeks
期刊介绍: Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.
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