Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials

Alicia Dickenstein; Maria Isabel Herrero; Luis Felipe Tabera

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arXiv · 1601.05479

Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials

Alicia Dickenstein·Maria Isabel Herrero·Luis Felipe Tabera

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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.

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Alicia Dickenstein, Maria Isabel Herrero, Luis Felipe Tabera. 2016-01-21. Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials. https://arxiv.org/abs/1601.05479

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