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math.AG2026
Permuting the roots of univariate polynomials whose coefficients depend on parameters
Alexander Esterov, Lionel Lang
We address two interrelated problems concerning the permutation of roots of univariate polynomials whose coefficients depend on parameters. First, we compute the Galois group of po…
math.AG2025
Bernstein-Kouchnirenko-Khovanskii with a symmetry
Alexander Esterov, Lionel Lang
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 ir…
math.AG2024
Gauss--Bonnet for CSM classes of very affine manifolds, and tropical isotopies
Alexander Esterov
The CSM class of a very affine manifold is represented by the rank drop locus of a general tuple of torus invariant 1-forms on it. This equality holds in the homology of any to…