Maximal Brill-Noether loci via degenerations and double covers
- 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 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≤⌈g/2⌉ 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.
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| Author: | Andrei Viorel BudORCiDGND, Richard HaburcakORCiD |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-857480 |
| URL: | https://arxiv.org/abs/2404.15066v1 |
| DOI: | https://doi.org/10.48550/arXiv.2404.15066 |
| ArXiv Id: | http://arxiv.org/abs/2404.15066 |
| Parent Title (English): | arXiv |
| Publisher: | arXiv |
| Document Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2024/04/23 |
| Date of first Publication: | 2024/04/23 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2024/07/11 |
| Issue: | 2404.15066v1 |
| Edition: | Version 1 |
| Page Number: | 16 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
