BernsteinKouchnirenkoKhovanskii with a symmetry
Abstract
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 oneparameter families of complex univariate polynomials, whose Galois group is a complete symmetric group.
 Publication:

arXiv eprints
 Pub Date:
 July 2022
 DOI:
 10.48550/arXiv.2207.03923
 arXiv:
 arXiv:2207.03923
 Bibcode:
 2022arXiv220703923E
 Keywords:

 Mathematics  Algebraic Geometry;
 14M25
 EPrint:
 29 pages, 5 figures