On rank 3 quadratic equations of Veronese embeddings

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-08-04 DOI:10.1002/mana.70028

Euisung Park, Saerom Sim

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引用次数: 0

Abstract

This paper studies the geometric structure of the locus $Φ_{3} (X)$ of rank 3 quadratic equations of the Veronese variety $X = ν_{d} (P^{n})$ . Specifically, we investigate the minimal irreducible decomposition of $Φ_{3} (X)$ of rank 3 quadratic equations and analyze the geometric properties of the irreducible components of $Φ_{3} (X)$ such as their desingularizations. Additionally, we explore the non-singularity and singularity of these irreducible components of $Φ_{3} (X)$ .

查看原文本刊更多论文

关于Veronese嵌入的3阶二次方程

本文研究了Veronese变量X = ν的3阶二次方程的轨迹Φ 3 (X) $\Phi _3 (X)$的几何结构d (pn) $X = \nu _d ({\mathbb {P}}^n)$。具体来说，研究了3阶二次方程Φ 3 (X) $\Phi _3 (X)$的最小不可约分解，并分析了Φ不可约分量的几何性质3 (X) $\Phi _3 (X)$例如它们的去具体化。此外，我们还探讨了Φ 3 (X) $\Phi _3 (X)$的这些不可约分量的非奇异性和奇异性。

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index