Bernstein-Kouchnirenko-Khovanskii with a symmetry
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...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2207.03923 |