The geproci property in positive characteristic

IF 0.8 3区数学 Q2 MATHEMATICS Proceedings of the American Mathematical Society Pub Date : 2024-02-29 DOI:10.1090/proc/16809

Jake Kettinger

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Abstract

The geproci property is a recent development in the world of geometry. We call a set of points Z ⊆ P k 3 Z\subseteq \mathbb {P}_k^3 an ( a , b ) (a,b) -geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P P to a plane is a complete intersection of curves of degrees a ≤ b a\leq b . Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids.

In this paper, based partly on the author’s thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids.

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正特征中的 geproci 性质

geproci 属性是几何学领域的最新发展。如果一个点集 Z ⊆ P k 3 Z\subseteq \mathbb {P}_k^3 是一个（a , b ）（a,b）-geproci 集（GEneral PROjection is a Complete Intersection 的缩写），而它从一般点 P P 到平面的投影是 a≤b a\leq b 的度数的曲线的完全交集，我们就称这个点集为 geproci 集。早在 2011 年，人们就知道了被称为网格的非enerate 例子。2018 年首次描述了非enerate 非网格，在特征 0 下工作。几乎所有这些新例子都属于一种特殊类型，称为半网格。在本文中，我们部分基于作者的论文，利用正特征几何的一个特点，给出了产生geproci半网格和非半网格的新方法。

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

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 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 shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, 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. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.