INVESTIGADORES
DICKENSTEIN Alicia Marcela
artículos
Título:
Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials
Autor/es:
A. DICKENSTEIN, M. I. HERRERO, L. F. TABERA
Revista:
ISRAEL JOURNAL OF MATHEMATICS
Editorial:
HEBREW UNIV MAGNES PRESS
Referencias:
Lugar: Jerusalem; Año: 2017 vol. 221 p. 741 - 777
ISSN:
0021-2172
Resumen:
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.