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Abstract:

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.

Registro:

Documento: Artículo
Título:Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials
Autor:Dickenstein, A.; Herrero, M.I.; Tabera, L.F.
Filiación:Dto. de Matemática, FCEN, Universidad de Buenos Aires, Pab. I - C1428EGA, Buenos Aires, Argentina
IMAS (UBA-CONICET), Ciudad Universitaria, Pab. I - C1428EGA, Buenos Aires, Argentina
Dto. Matemáticas, Estadística y Computación, Universidad de Cantabria, Cantabria, Spain
Año:2017
Volumen:221
Número:2
Página de inicio:741
Página de fin:777
DOI: http://dx.doi.org/10.1007/s11856-017-1573-0
Título revista:Israel Journal of Mathematics
Título revista abreviado:Isr. J. Math.
ISSN:00212172
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00212172_v221_n2_p741_Dickenstein

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Citas:

---------- APA ----------
Dickenstein, A., Herrero, M.I. & Tabera, L.F. (2017) . Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials. Israel Journal of Mathematics, 221(2), 741-777.
http://dx.doi.org/10.1007/s11856-017-1573-0
---------- CHICAGO ----------
Dickenstein, A., Herrero, M.I., Tabera, L.F. "Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials" . Israel Journal of Mathematics 221, no. 2 (2017) : 741-777.
http://dx.doi.org/10.1007/s11856-017-1573-0
---------- MLA ----------
Dickenstein, A., Herrero, M.I., Tabera, L.F. "Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials" . Israel Journal of Mathematics, vol. 221, no. 2, 2017, pp. 741-777.
http://dx.doi.org/10.1007/s11856-017-1573-0
---------- VANCOUVER ----------
Dickenstein, A., Herrero, M.I., Tabera, L.F. Arithmetics and combinatorics of tropical Severi varieties of univariate polynomials. Isr. J. Math. 2017;221(2):741-777.
http://dx.doi.org/10.1007/s11856-017-1573-0