Hermitian-einstein metrics on parabolic stable bundles |
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Authors: | Jiayu Li M S Narasimhan |
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Institution: | (1) Institute of Mathematics, Academia Sinica, 100080 Beijing, P. R. China;(2) Mathematics Section, International Centre for Theoretic Physics, P.O.Box 586, 34100 Trieste, Italy |
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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 the existence of a metric on $E'{\text{ = }}E|_{\overline M \backslash D} $ (compatible with the parabolic structure) which is Hermitian-Einstein with respect to the restriction of the Kähler metric to $\overline M $ ěD. A converse is also proved. |
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Keywords: | Hermitian-Einstein metric Parabolic stable bundle K?hler manifold |
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