Hermitian-Einstein Metrics on Parabolic Bundles over compact complex surfaces | Synapse
October 20, 2025Open Access
Hermitian-Einstein Metrics on Parabolic Bundles over compact complex surfaces
Key Points
The correspondence shows a deep relationship between geometry and stability in parabolic bundles.
It establishes the Kobayashi-Hitchin correspondence for nonKähler surfaces with specific divisor conditions.
The methods apply to both simple normal crossing divisors and smooth divisors in various dimensions.
This work highlights new avenues for exploring geometrical structures in complex manifolds.
Abstract
We prove the Kobayashi-Hitchin correspondence for parabolic bundles over compact nonKähler surfaces with simple normal crossing divisor or compact nonKähler manifolds of any dimension with smooth divisor.