非厄米杨--米尔斯联络与消失的陈类
Non-Hermitian Yang--Mills Connections with Vanishing Chern Classes
浏览论文内容
中文总结 AI 辅助
本文在紧致Kähler曲面的光滑平凡二秩丛上构造了非平坦非厄米杨--米尔斯联络，其陈类为零且两侧稳定，表明消失陈类不强制平坦性，并给出模空间收缩与能量估计。
中文摘要 AI 辅助
我们在紧致Kähler曲面上光滑平凡的二秩向量丛上构造了具有零爱因斯坦常数的非平坦非厄米杨--米尔斯联络，这些联络具有正调和度量，并且诱导和伴随的全纯丛是稳定的。因此，即使在两侧都满足稳定性的条件下，消失的陈类也不强制平坦性。局部模型来自已知的复反自对偶ansatz；稳定的下降产生了显式的全局模空间现象。对于固定的稳定丛，Kaledin--Verbitsky映射在Hermitian--Einstein联络的连通分量中收缩一条包含平坦和非平坦点的复线。在两侧稳定轨迹中也发生收缩。全纯投影对的一个纤维同时包含平坦和非平坦点。一个能量恒等式和一个谱间隙估计在固定诱导全纯结构的情况下量化了局部平坦性。
英文摘要
We construct non-flat non-Hermitian Yang--Mills connections with zero Einstein constant on smoothly trivial rank-two bundles over compact Kähler surfaces, with positive harmonic metrics and stable induced and adjoint holomorphic bundles. Thus vanishing Chern classes do not force flatness even under stability on both sides. The local model comes from a known complex anti-self-dual ansatz; the stable descents yield explicit global moduli phenomena. For a fixed stable bundle, the Kaledin--Verbitsky map contracts a complex line containing flat and non-flat points in the connected component of the Hermitian--Einstein connection. Contraction also occurs in the two-sided stable locus. The pair of holomorphic projections has a fibre containing both flat and non-flat points. An energy identity and a spectral-gap estimate quantify local flatness with the induced holomorphic structure fixed.
发表机构
- Zhejiang International Studies University（浙江外国语学院）
机构由 AI 辅助整理，请以论文原文为准。
