Abstract
Let \({\overline M}\) be a compact complex manifold of complex dimension two with a smooth Kähler metric and D a smooth divisor on \({\overline M}\). If E is a rank 2 holomorphic vector bundle on \({\overline M}\) with a stable parabolic structure along D, we prove that there exista a Hermitian-Einstein metric on \(E\prime = E\vert_{{\overline M}\backslash D}\) compatible with the parabolic structure, whose curvature is square integrable.
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Supported by the NSF of China
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Li, J.Y., Narasimhan, M.S. A Note on Hermitian-Einstein Metrics on Parabolic Stable Bundles. Acta Math Sinica 17, 77–80 (2001). https://doi.org/10.1007/s101140000091
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DOI: https://doi.org/10.1007/s101140000091