Abel–Jacobi map and curvature of the pulled back metric
Let X be a compact connected Riemann surface of genus at least two. The Abel–Jacobi map φ:Symd(X)→Picd(X) is an embedding if d is less than the gonality of X. We investigate the curvature of the pull-back, by φ, of the flat metric on Picd(X). In particular, we show that when d = 1, the curvature is...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2021-04-01
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| Series: | Bulletin of Mathematical Sciences |
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| Online Access: | http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500149 |
| Summary: | Let X be a compact connected Riemann surface of genus at least two. The Abel–Jacobi map φ:Symd(X)→Picd(X) is an embedding if d is less than the gonality of X. We investigate the curvature of the pull-back, by φ, of the flat metric on Picd(X). In particular, we show that when d = 1, the curvature is strictly negative everywhere if X is not hyperelliptic, and when X is hyperelliptic, the curvature is nonpositive with vanishing exactly on the points of X fixed by the hyperelliptic involution. |
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| ISSN: | 1664-3607 1664-3615 |