Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials
Algebraic Geometry
2016-09-13 v3 Combinatorics
Abstract
We give a description of the tropical variety of univariate polynomials of degree n having two double roots. As a set, it is given as the union of three types of maximal cones of dimension n-1, where only cones of two of these types are cones of the secondary fan of {0,...,n}. Through Kapranov's theorem, this goal is achieved by a careful study of the possible valuations of the elementary symmetric functions of the roots of a polynomial with two double root. Despite its apparent simplicity, the computation of the tropical Severi variety has both combinatorial and arithmetic ingredients.
Keywords
Cite
@article{arxiv.1601.05479,
title = {Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials},
author = {Alicia Dickenstein and Maria Isabel Herrero and Luis Felipe Tabera},
journal= {arXiv preprint arXiv:1601.05479},
year = {2016}
}
Comments
24 pages, 5 figures. Minor improvements