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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.13084 |
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| _version_ | 1866929617961484288 |
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| author | Jing, Yifan Zou, Tingxiang |
| author_facet | Jing, Yifan Zou, Tingxiang |
| contents | We establish a group-action version of the Szemerédi-Trotter theorem over any field, extending Bourgain's result for the group $\mathrm{SL}_2(k)$. As an Elekes-Szabó-type application, we obtain quantitative bounds on the number of collinear triples on reducible cubic surfaces in $\mathbb{P}^3(k)$, where $k = \mathbb{F}_{q}$ and $k = \mathbb{C}$, thereby improving a recent result by Bays, Dobrowolski, and the second author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13084 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A group-action Szemerédi-Trotter theorem and applications to orchard problems in all characteristics Jing, Yifan Zou, Tingxiang Combinatorics We establish a group-action version of the Szemerédi-Trotter theorem over any field, extending Bourgain's result for the group $\mathrm{SL}_2(k)$. As an Elekes-Szabó-type application, we obtain quantitative bounds on the number of collinear triples on reducible cubic surfaces in $\mathbb{P}^3(k)$, where $k = \mathbb{F}_{q}$ and $k = \mathbb{C}$, thereby improving a recent result by Bays, Dobrowolski, and the second author. |
| title | A group-action Szemerédi-Trotter theorem and applications to orchard problems in all characteristics |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.13084 |