Maximal Brill--Noether loci via the gonality stratification
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913380382539776 |
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| author | Auel, Asher Haburcak, Richard Larson, Hannah |
| author_facet | Auel, Asher Haburcak, Richard Larson, Hannah |
| contents | We study the restriction of Brill-Noether loci to the gonality stratification of the moduli space of curves of fixed genus. As an application, we give new proofs that Brill-Noether loci with $ρ=-1$ have distinct support, and for fixed $r$ give lower bounds on when one direction of the non-containments of the Maximal Brill-Noether Loci Conjecture hold for Brill-Noether loci of rank $r$ linear systems. Using these techniques, we also show that Brill-Noether loci corresponding to rank $2$ linear systems are maximal as soon as $g\ge 28$ and prove the Maximal Brill-Noether Loci Conjecture for $g=20$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_09954 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximal Brill--Noether loci via the gonality stratification Auel, Asher Haburcak, Richard Larson, Hannah Algebraic Geometry 14H51 We study the restriction of Brill-Noether loci to the gonality stratification of the moduli space of curves of fixed genus. As an application, we give new proofs that Brill-Noether loci with $ρ=-1$ have distinct support, and for fixed $r$ give lower bounds on when one direction of the non-containments of the Maximal Brill-Noether Loci Conjecture hold for Brill-Noether loci of rank $r$ linear systems. Using these techniques, we also show that Brill-Noether loci corresponding to rank $2$ linear systems are maximal as soon as $g\ge 28$ and prove the Maximal Brill-Noether Loci Conjecture for $g=20$. |
| title | Maximal Brill--Noether loci via the gonality stratification |
| topic | Algebraic Geometry 14H51 |
| url | https://arxiv.org/abs/2310.09954 |