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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2021-04-01
|
| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500149 |
| _version_ | 1818618060341248000 |
|---|---|
| author | Indranil Biswas |
| author_facet | Indranil Biswas |
| author_sort | Indranil Biswas |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-16T17:15:35Z |
| format | Article |
| id | doaj.art-0191b6945e4f4ce39022f47d5a2ceef8 |
| institution | Directory Open Access Journal |
| issn | 1664-3607 1664-3615 |
| language | English |
| last_indexed | 2024-12-16T17:15:35Z |
| publishDate | 2021-04-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj.art-0191b6945e4f4ce39022f47d5a2ceef82022-12-21T22:23:18ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152021-04-011112050014-12050014-710.1142/S166436072050014910.1142/S1664360720500149Abel–Jacobi map and curvature of the pulled back metricIndranil Biswas0School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, IndiaLet 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.http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500149gonalitycurvaturesymmetric productabel–jacobi map |
| spellingShingle | Indranil Biswas Abel–Jacobi map and curvature of the pulled back metric Bulletin of Mathematical Sciences gonality curvature symmetric product abel–jacobi map |
| title | Abel–Jacobi map and curvature of the pulled back metric |
| title_full | Abel–Jacobi map and curvature of the pulled back metric |
| title_fullStr | Abel–Jacobi map and curvature of the pulled back metric |
| title_full_unstemmed | Abel–Jacobi map and curvature of the pulled back metric |
| title_short | Abel–Jacobi map and curvature of the pulled back metric |
| title_sort | abel jacobi map and curvature of the pulled back metric |
| topic | gonality curvature symmetric product abel–jacobi map |
| url | http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500149 |
| work_keys_str_mv | AT indranilbiswas abeljacobimapandcurvatureofthepulledbackmetric |