Bernstein-Kouchnirenko-Khovanskii with a symmetry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908501010284544 |
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| author | Esterov, Alexander Lang, Lionel |
| author_facet | Esterov, Alexander Lang, Lionel |
| contents | A generic polynomial f(x,y,z) with a prescribed Newton polytope defines a symmetric spatial curve f(x,y,z)=f(y,x,z)=0. We study its geometry: the number, degree and genus of its irreducible components, the number and type of singularities, etc. and discuss to what extent these results generalize to higher dimension and more complicated symmetries.
As an application, we characterize generic one-parameter families of complex univariate polynomials, whose Galois group is a complete symmetric group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03923 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bernstein-Kouchnirenko-Khovanskii with a symmetry Esterov, Alexander Lang, Lionel Algebraic Geometry 14M25 A generic polynomial f(x,y,z) with a prescribed Newton polytope defines a symmetric spatial curve f(x,y,z)=f(y,x,z)=0. We study its geometry: the number, degree and genus of its irreducible components, the number and type of singularities, etc. and discuss to what extent these results generalize to higher dimension and more complicated symmetries. As an application, we characterize generic one-parameter families of complex univariate polynomials, whose Galois group is a complete symmetric group. |
| title | Bernstein-Kouchnirenko-Khovanskii with a symmetry |
| topic | Algebraic Geometry 14M25 |
| url | https://arxiv.org/abs/2207.03923 |