Multiple Lines of Maximum Genus in $\mathbb{P}^3$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910773585903616 |
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| author | Schlesinger, Enrico |
| author_facet | Schlesinger, Enrico |
| contents | We introduce a notion of good cohomology for multiple lines in $\mathbb{P}^3$ and we classify multiple lines with good cohomology up to multiplicity 4. In particular, we show that the family of space curves of degree d, not lying on a surface of degree less than d, and of maximal arithmetic genus is not irreducible already for d=4 and d=5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple Lines of Maximum Genus in $\mathbb{P}^3$ Schlesinger, Enrico Algebraic Geometry Commutative Algebra 14H50, 14F06, 14F17 We introduce a notion of good cohomology for multiple lines in $\mathbb{P}^3$ and we classify multiple lines with good cohomology up to multiplicity 4. In particular, we show that the family of space curves of degree d, not lying on a surface of degree less than d, and of maximal arithmetic genus is not irreducible already for d=4 and d=5. |
| title | Multiple Lines of Maximum Genus in $\mathbb{P}^3$ |
| topic | Algebraic Geometry Commutative Algebra 14H50, 14F06, 14F17 |
| url | https://arxiv.org/abs/2501.02574 |