Surface counterexamples to the Eisenbud-Goto conjecture

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-04-19 DOI:10.1090/tran/9192

Jong In Han, Sijong Kwak

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引用次数: 0

Abstract

It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in P 5 \mathbb {P}^5 , and toric varieties of codimension two. After J. McCullough and I. Peeva constructed counterexamples in 2018, it has been an interesting question to find the categories such that the Eisenbud-Goto conjecture holds. So far, surface counterexamples have not been found while counterexamples of any dimension greater or equal to 3 are known.

In this paper, we construct counterexamples to the Eisenbud-Goto conjecture for projective surfaces in P 4 \mathbb {P}^4 and investigate projective invariants, cohomological properties, and geometric properties. The counterexamples are constructed via binomial rational maps between projective spaces.

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艾森布-后藤猜想的曲面反例

众所周知，艾森布德-戈托正则猜想对于算术上的科恩-麦考莱（Cohen-Macaulay）变体、投影曲线、光滑曲面、P 5 \mathbb {P}^5 中的光滑三褶，以及标度为二的环状变体都是成立的。在 J. McCullough 和 I. Peeva 于 2018 年构造出反例之后，如何找到艾森布德-后藤猜想成立的范畴一直是一个有趣的问题。迄今为止，尚未发现曲面反例，而已知任何维度大于或等于3的反例。在本文中，我们为 P 4 \mathbb {P}^4 中的投影面构造了艾森布德-后藤猜想的反例，并研究了投影不变式、同调性质和几何性质。反例是通过投影空间之间的二项式有理映射构造的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 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 in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.