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 |
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paper:paper_00212172_v221_n2_p741_Dickenstein2023-06-08T14:42:03Z 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 {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. 2017 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 |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| title |
Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials |
| spellingShingle |
Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials |
| title_short |
Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials |
| title_full |
Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials |
| title_fullStr |
Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials |
| title_full_unstemmed |
Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials |
| title_sort |
arithmetics and combinatorics of tropical severi varieties of univariate polynomials |
| publishDate |
2017 |
| url |
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 |
| _version_ |
1768541689751797760 |