Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials

A. DICKENSTEIN, M. I. HERRERO, L. F. TABERA

ISRAEL JOURNAL OF MATHEMATICS

HEBREW UNIV MAGNES PRESS

Lugar: Jerusalem; Año: 2017 vol. 221 p. 741 - 777

0021-2172

We give a description of the tropical variety of univariate polynomials ofdegree n having two double roots. As a set, it is given as the union of threetypes of maximal cones of dimension n-1, where only cones of two of these typesare cones of the secondary fan of {0,...,n}. Through Kapranov´s theorem, thisgoal is achieved by a careful study of the possible valuations of theelementary symmetric functions of the roots of a polynomial with two doubleroot. Despite its apparent simplicity, the computation of the tropical Severivariety has both combinatorial and arithmetic ingredients.