Rational and lacunary algebraic curves
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910294155984896 |
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| author | Comte, Georges Tavenas, Sébastien |
| author_facet | Comte, Georges Tavenas, Sébastien |
| contents | We give a bound on the number $\mathcal{Z}$ of intersection points in a ball of the complex plane, between a rational curve and a lacunary algebraic curve $Q=0$. This bound depends only on the lacunarity diagram of $Q$, and in particular is uniform in the coefficients of $Q$. Our bound shows that $\mathcal{Z}=O(dm)$, where $d$ is the degree of $Q$ and $m$ is the number of its monomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational and lacunary algebraic curves Comte, Georges Tavenas, Sébastien Algebraic Geometry Complex Variables 14H50, 14Q05 We give a bound on the number $\mathcal{Z}$ of intersection points in a ball of the complex plane, between a rational curve and a lacunary algebraic curve $Q=0$. This bound depends only on the lacunarity diagram of $Q$, and in particular is uniform in the coefficients of $Q$. Our bound shows that $\mathcal{Z}=O(dm)$, where $d$ is the degree of $Q$ and $m$ is the number of its monomials. |
| title | Rational and lacunary algebraic curves |
| topic | Algebraic Geometry Complex Variables 14H50, 14Q05 |
| url | https://arxiv.org/abs/2401.05512 |