关于皮卡数为 1 的有理同素变种上的等变向量束的完全相交超卡勒四折

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-10-30 DOI:10.1016/j.geomphys.2024.105348

Eunjeong Lee , Kyeong-Dong Park

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引用次数: 0

摘要

我们对皮卡尔数为 1 的特殊同素异形体上的完全可还原等向向量束的一般全局截面的零点位置的具有琐碎典型束的四叠体进行了分类。通过计算它们的霍奇数，我们发现其中不存在超卡勒四折。这意味着，作为皮卡尔数为 1 的有理均相变上的完全可还原等向向量束的一般全局截面的零点位置所表示的超卡勒四重是博维尔-多纳吉和德巴勒-沃桑所描述的两种情况之一。

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Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one

We classify fourfolds with trivial canonical bundle which are zero loci of general global sections of completely reducible equivariant vector bundles over exceptional homogeneous varieties of Picard number one. By computing their Hodge numbers, we see that there exist no hyperkähler fourfolds among them. This implies that a hyperkähler fourfold represented as the zero locus of a general global section of a completely reducible equivariant vector bundle over a rational homogeneous variety of Picard number one is one of the two cases described by Beauville–Donagi and Debarre–Voisin.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

期刊最新文献

Editorial Board On conformal collineation and almost Ricci solitons Cohomology and extensions of relative Rota–Baxter groups Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one