Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908278048423936 |
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| author | Moretti, Federico |
| author_facet | Moretti, Federico |
| contents | In this paper we compute the gonality and the dimension of the Brill-Noether loci $W^1_d(C)$ for curves in a non primitive linear system of a simple abelian surface, adapting vector bundles techniques à la Lazarsfeld originally introduced with $K3$ surfaces. As a corollary, we obtain general Green's conjecture for curves on abelian surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_15977 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces Moretti, Federico Algebraic Geometry 14H51, 14J60 In this paper we compute the gonality and the dimension of the Brill-Noether loci $W^1_d(C)$ for curves in a non primitive linear system of a simple abelian surface, adapting vector bundles techniques à la Lazarsfeld originally introduced with $K3$ surfaces. As a corollary, we obtain general Green's conjecture for curves on abelian surfaces. |
| title | Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces |
| topic | Algebraic Geometry 14H51, 14J60 |
| url | https://arxiv.org/abs/2205.15977 |