Linear system of geometrically irreducible plane cubics over finite fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917875243024384 |
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| author | Asgarli, Shamil Ghioca, Dragos |
| author_facet | Asgarli, Shamil Ghioca, Dragos |
| contents | We examine the maximum dimension of a linear system of plane cubic curves whose $\mathbb{F}_q$-members are all geometrically irreducible. Computational evidence suggests that such a system has a maximum (projective) dimension of $3$. As a step towards the conjecture, we prove that there exists a $3$-dimensional linear system $\mathcal{L}$ with at most one geometrically reducible $\mathbb{F}_q$-member. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear system of geometrically irreducible plane cubics over finite fields Asgarli, Shamil Ghioca, Dragos Algebraic Geometry Primary 14N05, Secondary 14C21, 14H50, 14G15 We examine the maximum dimension of a linear system of plane cubic curves whose $\mathbb{F}_q$-members are all geometrically irreducible. Computational evidence suggests that such a system has a maximum (projective) dimension of $3$. As a step towards the conjecture, we prove that there exists a $3$-dimensional linear system $\mathcal{L}$ with at most one geometrically reducible $\mathbb{F}_q$-member. |
| title | Linear system of geometrically irreducible plane cubics over finite fields |
| topic | Algebraic Geometry Primary 14N05, Secondary 14C21, 14H50, 14G15 |
| url | https://arxiv.org/abs/2407.18104 |