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Projective embedding
of stably degenerating sequences of hyperbolic Riemann
surfaces
Jingzhou Sun |
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Vol. 17 (2024), No. 6, 1871–1886
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Abstract |
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Given a sequence of genus curves converging to a punctured Riemann surface with complete metric of constant Gaussian curvature , we prove that the Kodaira embedding using an orthonormal basis of the Bergman space of sections of a pluricanonical bundle also converges to the embedding of the limit space together with extra complex projective lines. |
Keywords
stable degeneration, projective embedding, hyperbolic
metric
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Mathematical Subject Classification
Primary: 14H15, 30F10, 30F60
Secondary: 30F45
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Milestones
Received: 27 July 2020
Revised: 23 May 2022
Accepted: 22 November 2022
Published: 19 July 2024
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Authors |
| Jingzhou Sun | |
| Department of Mathematics Shantou University Shantou City, Guangdong China |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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