Maximal Brill-Noether loci via degenerations and double covers
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916684276695040 |
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| author | Bud, Andrei Haburcak, Richard |
| author_facet | Bud, Andrei Haburcak, Richard |
| contents | Using limit linear series on chains of curves, we show that closures of certain Brill--Noether loci contain a product of pointed Brill--Noether loci of small codimension. As a result, we obtain new non-containments of Brill--Noether loci, in particular that all dimensionally expected non-containments hold for expected maximal Brill--Noether loci. Using these degenerations, we also give a new proof that Brill--Noether loci with expected codimension $-ρ\leq \lceil g/2\rceil$ have a component of the expected dimension. Additionally, we obtain new non-containments of Brill--Noether loci by considering the locus of the source curves of unramified double covers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal Brill-Noether loci via degenerations and double covers Bud, Andrei Haburcak, Richard Algebraic Geometry 14H51, 14H10 Using limit linear series on chains of curves, we show that closures of certain Brill--Noether loci contain a product of pointed Brill--Noether loci of small codimension. As a result, we obtain new non-containments of Brill--Noether loci, in particular that all dimensionally expected non-containments hold for expected maximal Brill--Noether loci. Using these degenerations, we also give a new proof that Brill--Noether loci with expected codimension $-ρ\leq \lceil g/2\rceil$ have a component of the expected dimension. Additionally, we obtain new non-containments of Brill--Noether loci by considering the locus of the source curves of unramified double covers. |
| title | Maximal Brill-Noether loci via degenerations and double covers |
| topic | Algebraic Geometry 14H51, 14H10 |
| url | https://arxiv.org/abs/2404.15066 |