塌缩椭圆纤维K3曲面上的Hermitian-Yang-Mills连接。

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of Geometric Analysis Pub Date : 2022-01-01 Epub Date: 2022-01-07 DOI:10.1007/s12220-021-00808-9

Ved Datar, Adam Jacob

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引用次数: 2

摘要

设X→p1是一个椭圆纤维的K3曲面，允许一个序列ω i的ricci平面度量使纤维坍缩。设V是X上的全纯SU(n)束，对ω i稳定。给定V上的Hermitian-Yang-Mills连接的对应序列Ξ i，证明了当E是一般光纤时，限制序列Ξ i | E收敛于平面连接a 0。更进一步，如果约束V | E的形式为⊕j = 1n O E (q j - 0)对于n个不同的点q j∈E，则这些点唯一地决定了A 0。

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Hermitian-Yang-Mills Connections on Collapsing Elliptically Fibered K3 Surfaces.

Let $X \to P^{1}$ be an elliptically fibered K3 surface, admitting a sequence $ω_{i}$ of Ricci-flat metrics collapsing the fibers. Let V be a holomorphic SU(n) bundle over X, stable with respect to $ω_{i}$ . Given the corresponding sequence $Ξ_{i}$ of Hermitian-Yang-Mills connections on V, we prove that, if E is a generic fiber, the restricted sequence $Ξ_{i} |_{E}$ converges to a flat connection $A_{0}$ . Furthermore, if the restriction ${V |}_{E}$ is of the form $\oplus_{j = 1}^{n} O_{E} (q_{j} - 0)$ for n distinct points $q_{j} \in E$ , then these points uniquely determine $A_{0}$ .

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来源期刊

Journal of Geometric Analysis 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

290

审稿时长

3 months

期刊介绍： JGA publishes both research and high-level expository papers in geometric analysis and its applications. There are no restrictions on page length.