\(F_4\) and desmic quartic surfaces

IF 0.8 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2026-02-02 DOI:10.1007/s10455-026-10028-5

Laurent Manivel

引用次数: 0

Abstract

The desmic pencil of quartic surfaces is part of a beautiful, but mostly forgotten chapter of the classical theory of algebraic surfaces: it is the only non-degenerate pencil of quartic surfaces in \({\mathbb {P}}^3\) containing at least three completely reducible members. We observe in this note that it is closely related to the Weyl group of the root system \(F_4\), and can be recovered from a series of symmetric spaces deduced from the exceptional Lie algebras. We discuss the main properties of the pencil from this Lie theoretic point of view.

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\(F_4\) 以及大地四次曲面

四次曲面的半简并铅笔是经典代数曲面理论中一个美丽的，但几乎被遗忘的章节的一部分：它是\({\mathbb {P}}^3\)中唯一一个包含至少三个完全可约成员的四次曲面的非简并铅笔。我们注意到它与根系\(F_4\)的Weyl群密切相关，并且可以从一系列由例外李代数推导的对称空间中恢复。我们从李论的角度讨论了铅笔的主要性质。

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

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.