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Admissible Hermitian
metrics on families of line bundles over certain degenerating
Riemann surfaces
Wing-Keung To and Lin Weng |
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Vol. 197 (2001), No. 2, 441–489
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Abstract |
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We show that a family of line bundles of degree zero over a plumbing family of Riemann surfaces with a separating (resp. non-separating) node p admits a nice (resp. almost nice) family of flat p-singular Hermitian metrics. As a consequence, we give necessary and sufficient conditions for a family of line bundles over such families of Riemann surfaces to admit an (almost) nice family of p-singular Hermitian metrics which are admissible with respect to the canonical/hyperbolic (1,1)-forms on the Riemann surfaces. |
Milestones
Received: 21 July 1998
Revised: 30 May 2000
Published: 1 February 2001
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Authors |
| Wing-Keung To | |
| Department of Mathematics National University of Singapore 10 Kent Ridge Crescent Singapore 119260 |
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| Lin Weng | |
| Graduate School of Mathematics Nagoya University Chikusa-ku, Nagoya 464-8602 Japan |
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