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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00212172_v221_n2_p741_Dickenstein |
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todo:paper_00212172_v221_n2_p741_Dickenstein2023-10-03T14:20:48Z Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials Dickenstein, A. Herrero, M.I. Tabera, L.F. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 |
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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. |
| format |
JOUR |
| author |
Dickenstein, A. Herrero, M.I. Tabera, L.F. |
| spellingShingle |
Dickenstein, A. Herrero, M.I. Tabera, L.F. Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials |
| author_facet |
Dickenstein, A. Herrero, M.I. Tabera, L.F. |
| author_sort |
Dickenstein, A. |
| title |
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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00212172_v221_n2_p741_Dickenstein |
| work_keys_str_mv |
AT dickensteina arithmeticsandcombinatoricsoftropicalseverivarietiesofunivariatepolynomials AT herreromi arithmeticsandcombinatoricsoftropicalseverivarietiesofunivariatepolynomials AT taberalf arithmeticsandcombinatoricsoftropicalseverivarietiesofunivariatepolynomials |
| _version_ |
1807318379503026176 |