Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909221626314752 |
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| author | Datta, Mrinmoy Manna, Subrata |
| author_facet | Datta, Mrinmoy Manna, Subrata |
| contents | It was conjectured by Edoukou in 2008 that a non-degenerate Hermitian threefold in $\mathbb{P}^4 (\mathbb{F}_{q^2})$ has at most $d(q^5+q^2) + q^3 + 1$ points in common with a threefold of degree $d$ defined over $\mathbb{F}_{q^2}$. He proved the conjecture for $d=2$. In this paper, we show that the conjecture is true for $d = 3$ and $q \ge 7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold Datta, Mrinmoy Manna, Subrata Algebraic Geometry 14G05, 14G15, 05B25 It was conjectured by Edoukou in 2008 that a non-degenerate Hermitian threefold in $\mathbb{P}^4 (\mathbb{F}_{q^2})$ has at most $d(q^5+q^2) + q^3 + 1$ points in common with a threefold of degree $d$ defined over $\mathbb{F}_{q^2}$. He proved the conjecture for $d=2$. In this paper, we show that the conjecture is true for $d = 3$ and $q \ge 7$. |
| title | Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold |
| topic | Algebraic Geometry 14G05, 14G15, 05B25 |
| url | https://arxiv.org/abs/2406.07326 |