艾森巴德-戈托正则性猜想的反例

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2017-01-01 DOI:10.1090/JAMS/891

J. McCullough, I. Peeva

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引用次数: 51

摘要

我们的主要定理表明非退化齐次素数理想的正则性不受任何次多项式函数的约束;这适用于任何领域k。特别是，我们提供了长期存在的规律性猜想的反例，也被称为Eisenbud-Goto猜想(1984)。我们介绍了一种方法，它从齐次理想I开始，产生一个素理想，它的射影维数、正则性、度、维数、深度和余维数都是用I的数值不变量来表示的。这种方法也与最近由Ananyan-Hochster解决的Stillman猜想的精神产生界有关。爱荷华州立大学数学系，艾姆斯，纽约州50011，美国康奈尔大学数学系，伊萨卡，纽约州14853，美国

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Counterexamples to the Eisenbud–Goto regularity conjecture

Our main theorem shows that the regularity of non-degenerate homogeneous prime ideals is not bounded by any polynomial function of the degree; this holds over any field k. In particular, we provide counterexamples to the longstanding Regularity Conjecture, also known as the Eisenbud-Goto Conjecture (1984). We introduce a method which, starting from a homogeneous ideal I, produces a prime ideal whose projective dimension, regularity, degree, dimension, depth, and codimension are expressed in terms of numerical invariants of I. The method is also related to producing bounds in the spirit of Stillman’s Conjecture, recently solved by Ananyan-Hochster. Mathematics Department, Iowa State University, Ames, IA 50011, USA Mathematics Department, Cornell University, Ithaca, NY 14853, USA

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.