Combinatorics of generic 5-degree polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917668692426752 |
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| author | Kochetkov, Yury |
| author_facet | Kochetkov, Yury |
| contents | We consider the space $P$ of generic complex 5-degree polynomials. Critical values of such polynomial, i.e. four points in the complex plane, either are vertices of a convex quadrangle $Q$, or vertices of a triangle $T$ with one point inside $T$. The inverse image of $Q$ is a tree-like connected structure of five ovals (a cactus). The inverse image of $T$ is also a cactus, but of four ovals. Transformations of cacti of the first type into cacti of the second type and vice versa allow one to represent the space $P$ as a ribbon bipartite graph of genus 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10594 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorics of generic 5-degree polynomials Kochetkov, Yury Combinatorics We consider the space $P$ of generic complex 5-degree polynomials. Critical values of such polynomial, i.e. four points in the complex plane, either are vertices of a convex quadrangle $Q$, or vertices of a triangle $T$ with one point inside $T$. The inverse image of $Q$ is a tree-like connected structure of five ovals (a cactus). The inverse image of $T$ is also a cactus, but of four ovals. Transformations of cacti of the first type into cacti of the second type and vice versa allow one to represent the space $P$ as a ribbon bipartite graph of genus 3. |
| title | Combinatorics of generic 5-degree polynomials |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.10594 |