AI 中文总结
本文延续此前关于nef且大的上同调类的Kobayashi-Hitchin对应研究，证明紧Kähler流形上全纯向量丛中对应这类上同调类的$T$-Yang-Mills流全局可解且在Uhlenbeck极限下收敛，并刻画了极限联络在丰沛轨迹上的复规范等价结构。
AI 中文摘要
在之前的论文\textit{Jin26}中，作者引入了适配流（adapted current）$T$和适配Hermitian-Einstein度量的概念，建立了nef且大的上同调类$\alpha$对应的Kobayashi-Hitchin对应。作为此前工作的延续，本文研究紧Kähler流形$X$上全纯向量丛$E$中、对应nef且大的上同调类$\alpha$的Yang-Mills流的可解性与收敛性。我们特别证明，Yang-Mills流在无穷远处的极限由$E$的全纯结构与nef且大的上同调类$\alpha$决定。更准确地说，固定$E$上的一个可积酉联络$A_0$，我们证明$E$上以$A_0$为初值的$T$-Yang-Mills流在所有时间上均可解，且在Uhlenbeck极限意义下收敛于一个$T$-Yang-Mills联络$A_{\infty}$。此外我们还证明，在$\alpha$的丰沛轨迹（ample locus）上，$A_{\infty}$与$E$的$\alpha^{n-1}$-Harder-Narasimhan-Seshadri过滤对应的分次层的各因子上、$T$-适配Hermitian-Einstein度量的Chern联络的直和复规范等价。
英文摘要
In the previous paper \cite{Jin26}, the author introduced the notions of an adapted current $T$ and an adapted Hermitian-Einstein metric to establish the Kobayashi-Hitchin correspondence for a nef and big class $α$. As a continuation of the previous work, this paper studies the solvability and the convergence of the Yang-Mills flow for a nef and big class $α$ on a holomorphic vector bundle $E$ over a compact Kähler manifold $X$. In particular, we show that the limit of the Yang-Mills flow at infinity is determined by the holomorphic structure of $E$ and the nef and big class $α$. More precisely, if we fix an integrable unitary connection $A_0$ on $E$, we show that the $T$-Yang-Mills flow on $E$ with initial condition $A_0$ is solvable for all time and it converges to a $T$-Yang-Mills connection $A_{\infty}$ in the sense of Uhlenbeck limit. Furthermore, we also show that, on the ample locus of $α$, $A_{\infty}$ is complex-gauge equivalent to the direct sum of the Chern connections of the $T$-adapted Hermitian-Einstein metrics on the factors of the graded sheaf associated with the $α^{n-1}$-Harder-Narasimhan-Seshadri filtration of $E$.
Comments38 pages. Comments are welcome
