Izvorni znanstveni članak

https://doi.org/10.3336/gm.61.1.05

The Hitchin–Kobayashi correspondence for quiver bundles over the non-compact affine Gauduchon manifold

Pan Zhang ; School of Mathematical Sciences, Anhui University, Hefei 230601, P.R. China
Meng-Qi Zheng ; School of Mathematical Sciences, Anhui University, Hefei 230601, P.R. China
Chang-Sheng Zhu ; School of Mathematical Sciences, Anhui University, Hefei 230601, P.R. China

Preuzmi JATS datoteku

Sažetak

The objective of this paper is to prove a broader, generalized version of the Hitchin–Kobayashi correspondence
for the twisted quiver bundle \(\mathcal{R}\) over the non-compact special affine Gauduchon manifold \((M, D, g, \nu)\).
On the one hand, we prove that the analytic \((\sigma,\tau)\)-stability on \(\mathcal{R}\) implies the existence of an affine \((\sigma,\tau)\)-Hermite–Einstein metric. On the other hand, we prove that the analytic \((\sigma,\tau)\)-semi-stability on \(\mathcal{R}\) implies the existence of approximate affine \((\sigma,\tau)\)-Hermite–Einstein structure. The proof of the theorems relies on the heat flow method, alongside the continuity approach by Uhlenbeck and Yau. To overcome the analytical obstacles brought by the structure of the quiver, we use the maximum and minimum values of some eigenvalues to define a new quantity \(\chi\). Based on the method of proof by contradiction, the quantity \(\chi\) can be used in the discussion of constructing weak quiver subbundles that contradict stability or semi-stability.

Ključne riječi

Quiver bundle; non-compact affine manifold; analytic \((\sigma,\tau)\)-stability; affine \((\sigma,\tau)\)-Hermite–Einstein

Hrčak ID:

348190

URI

https://hrcak.srce.hr/348190

Datum izdavanja:

26.7.2026.

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