均匀束上均质型品种 \(G_2\)

IF 0.7 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-10-03 DOI:10.1007/s10455-025-10022-3

Xinyi Fang

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引用次数: 0

摘要

本文研究了齐次变量\(G_2/P_1\cong \mathbb {Q}^5\)和\(G_2/P_2\)上的全纯向量束。我们证明了如果\(G_2/P_i~(i=1,2)\)上的一个2级向量束E对于特殊的直线族是一致的，那么E要么是直线束的直接和，要么是一个不可分解的2束，它在扭转之前是唯一的。因此，我们在\(\mathbb {Q}^5\)上给出了Cayley束的一个新的表征。

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Uniform bundles on the homogeneous varieties of type \(G_2\)

In this paper, we study holomorphic vector bundles on the homogeneous varieties \(G_2/P_1\cong \mathbb {Q}^5\) and \(G_2/P_2\). We prove that if a rank 2 vector bundle E on \(G_2/P_i~(i=1,2)\) is uniform with respect to the special family of lines, then E is either a direct sum of line bundles or an indecomposable 2-bundle, which is unique up to twist. As a consequence, we give a new characterization of the Cayley bundles on \(\mathbb {Q}^5\).

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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.