Brill--Noether loci in genus $\leq 12$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908455271399424 |
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| author | Haburcak, Richard |
| author_facet | Haburcak, Richard |
| contents | A refined Brill--Noether theory seeks to determine which linear series are admitted by a ``general'' curve in a particular Brill--Noether locus. However, as Brill--Noether loci are not irreducible in general, a coarse answer is given by the relative positions of Brill--Noether loci. Via an analysis of unstable Lazarsfeld--Mukai bundles on K3 surfaces, we distinguish Brill--Noether loci and provide expectations for the relative positions of Brill--Noether loci in general. Together with classical results, the refined Brill--Noether theory for curves of fixed gonality and on Hirzebruch surfaces, and explicit constructions, we identify the relative positions of all Brill--Noether loci in genus $g\leq 12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brill--Noether loci in genus $\leq 12$ Haburcak, Richard Algebraic Geometry 14H51, 14J28, 14H10 A refined Brill--Noether theory seeks to determine which linear series are admitted by a ``general'' curve in a particular Brill--Noether locus. However, as Brill--Noether loci are not irreducible in general, a coarse answer is given by the relative positions of Brill--Noether loci. Via an analysis of unstable Lazarsfeld--Mukai bundles on K3 surfaces, we distinguish Brill--Noether loci and provide expectations for the relative positions of Brill--Noether loci in general. Together with classical results, the refined Brill--Noether theory for curves of fixed gonality and on Hirzebruch surfaces, and explicit constructions, we identify the relative positions of all Brill--Noether loci in genus $g\leq 12$. |
| title | Brill--Noether loci in genus $\leq 12$ |
| topic | Algebraic Geometry 14H51, 14J28, 14H10 |
| url | https://arxiv.org/abs/2507.04902 |