(Non-)Extendability of Abel-Jacobi Maps
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915154903433216 |
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| author | Rosengarten, Zev |
| author_facet | Rosengarten, Zev |
| contents | We investigate the "natural" locus of definition of Abel-Jacobi maps. In particular, we show that, for a proper, geometrically reduced curve C -- not necessarily smooth -- the Abel-Jacobi map from the smooth locus C^{sm} into the Jacobian of C does not extend to any larger (separated, geometrically reduced) curve containing C^{sm} except under certain particular circumstances which we describe explicitly. As a consequence, we deduce that the Abel-Jacobi map has closed image except in certain explicitly described circumstances, and that it is always a closed embedding for irreducible curves not isomorphic to P^1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | (Non-)Extendability of Abel-Jacobi Maps Rosengarten, Zev Algebraic Geometry We investigate the "natural" locus of definition of Abel-Jacobi maps. In particular, we show that, for a proper, geometrically reduced curve C -- not necessarily smooth -- the Abel-Jacobi map from the smooth locus C^{sm} into the Jacobian of C does not extend to any larger (separated, geometrically reduced) curve containing C^{sm} except under certain particular circumstances which we describe explicitly. As a consequence, we deduce that the Abel-Jacobi map has closed image except in certain explicitly described circumstances, and that it is always a closed embedding for irreducible curves not isomorphic to P^1. |
| title | (Non-)Extendability of Abel-Jacobi Maps |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2404.02766 |