有限域上超曲面的横向线性子空间

IF 1.2 3区数学 Q1 MATHEMATICS Finite Fields and Their Applications Pub Date : 2024-02-28 DOI:10.1016/j.ffa.2024.102396

Shamil Asgarli , Lian Duan , Kuan-Wen Lai

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引用次数: 0

摘要

Ballico 证明，如果 q≥d(d-1)m ，则在 q 元素的有限域上，度数为 d、维数为 m 的光滑投影综 X 具有光滑超平面截面。在本文中，我们针对光滑超曲面上的高次元线性截面和弗罗贝尼斯经典超曲面上的超平面截面完善了这一准则。我们还证明了还原超曲面上还原超平面截面存在性的类似结果。

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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Transverse linear subspaces to hypersurfaces over finite fields

Ballico proved that a smooth projective variety X of degree d and dimension m over a finite field of q elements admits a smooth hyperplane section if $q \geq d {(d - 1)}^{m}$ . In this paper, we refine this criterion for higher codimensional linear sections on smooth hypersurfaces and for hyperplane sections on Frobenius classical hypersurfaces. We also prove a similar result for the existence of reduced hyperplane sections on reduced hypersurfaces.

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.

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