A criterion of containment for tropical hypersurfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911787078647808 |
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| author | Grigoriev, Dima |
| author_facet | Grigoriev, Dima |
| contents | For tropical $n$-variable polynomials $f, g$ a criterion of containment for tropical hypersurfaces $Trop(f)\subset Trop(g)$ is provided in terms of their Newton polyhedra $N(f), N(g)\subset \mathbb{R}^{n+1}$. Namely, $Trop(f)\subset Trop(g)$ iff for every vertex $v$ of $N(g)$ there exist a homothety $t\cdot N(f), t>0$ and a parallel shift $s:\mathbb{R}^{n+1} \to \mathbb{R}^{n+1}$ such that $v\in s(t\cdot N(f))\subset N(g)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_18384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A criterion of containment for tropical hypersurfaces Grigoriev, Dima Algebraic Geometry 14T05 For tropical $n$-variable polynomials $f, g$ a criterion of containment for tropical hypersurfaces $Trop(f)\subset Trop(g)$ is provided in terms of their Newton polyhedra $N(f), N(g)\subset \mathbb{R}^{n+1}$. Namely, $Trop(f)\subset Trop(g)$ iff for every vertex $v$ of $N(g)$ there exist a homothety $t\cdot N(f), t>0$ and a parallel shift $s:\mathbb{R}^{n+1} \to \mathbb{R}^{n+1}$ such that $v\in s(t\cdot N(f))\subset N(g)$. |
| title | A criterion of containment for tropical hypersurfaces |
| topic | Algebraic Geometry 14T05 |
| url | https://arxiv.org/abs/2402.18384 |