Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials
We give a description of the tropical Severi variety of univariate polynomials of degree n having two double roots. We show that, as a set, it is given as the union of three explicit types of cones of maximal dimension n − 1, where only cones of two of these types are cones of the secondary fan of {...
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2017
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00212172_v221_n2_p741_Dickenstein http://hdl.handle.net/20.500.12110/paper_00212172_v221_n2_p741_Dickenstein |
| Aporte de: |
| Sumario: | We give a description of the tropical Severi variety of univariate polynomials of degree n having two double roots. We show that, as a set, it is given as the union of three explicit types of cones of maximal 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 roots. Despite its apparent simplicity, the computation of the tropical Severi variety has both combinatorial and arithmetic ingredients. © 2017, Hebrew University of Jerusalem. |
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