Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal intersection points of planar tropical curves. © 2011 Springer Science+Business Media, LLC.

Registro:

Documento: Artículo
Título:Singular Tropical Hypersurfaces
Autor:Dickenstein, A.; Tabera, L.F.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, C1428EGA Buenos Aires, Argentina
Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39071 Santander, Spain
Palabras clave:Discriminant; Euler derivative; Singularity; Tropical geometry
Año:2012
Volumen:47
Número:2
Página de inicio:430
Página de fin:453
DOI: http://dx.doi.org/10.1007/s00454-011-9364-6
Título revista:Discrete and Computational Geometry
Título revista abreviado:Discrete Comput. Geom.
ISSN:01795376
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v47_n2_p430_Dickenstein

Referencias:

  • Ardila, F., Klivans, C.J., The Bergman complex of a matroid and phylogenetic trees (2006) J. Comb. Theory, Ser. B, 96 (1), pp. 38-49
  • Bogart, T., Jensen, A.N., Speyer, D., Sturmfels, B., Thomas, R.R., Computing tropical varieties (2007) J. Symb. Comput., 42 (1-2), pp. 54-73
  • Brugallé, E., López de Medrano, L., (2011) Inflection points of real and tropical plane curves, , arXiv: 1102. 2478
  • Dickenstein, A., Feichtner, E.M., Sturmfels, B., Tropical discriminants (2007) J. Am. Math. Soc., 20 (4), pp. 1111-1133. , (electronic)
  • Einsiedler, M., Kapranov, M., Lind, D., Non-Archimedean amoebas and tropical varieties (2006) J. Reine Angew. Math., 601, pp. 139-157
  • Esterov, A., Newton polyhedra of discriminants of projections (2010) Discrete Comput. Geom., 44 (1), pp. 96-148
  • Gel'fand, I.M., Kapranov, M.M., Zelevinsky, A.V., (1994) Discriminants, Resultants, and Multidimensional Determinants, , Mathematics: Theory & Applications, Boston: Birkhäuser
  • Izhakian, Z., Tropical arithmetic and matrix algebra (2009) Commun. Algebra, 37 (4), pp. 1445-1468
  • Izhakian, Z., Rowen, L., (2008) Supertropical algebra, , arXiv: 0806. 1175
  • Markwig, H., Markwig, T., Shustin, E., Tropical curves with a singularity in a fixed point, , arXiv: 0909. 1827 (2009)
  • Mikhalkin, G., Tropical geometry, , Draft of the book in preparation
  • Mikhalkin, G., Enumerative tropical algebraic geometry in ℝ 2 (2005) J. Am. Math. Soc., 18 (2), pp. 313-377. , (electronic)
  • Ochse, D., (2009) The relation between the tropical A-discriminant and the secondary fan
  • Sturmfels, B., (2002) Solving Systems of Polynomial Equations, 97. , CBMS Regional Conference Series in MathematicsPublished for the Conference Board of the Mathematical Sciences, Washington, DC
  • Tabera, L.F., Tropical plane geometric constructions: a transfer technique in tropical geometry (2011) Rev. Mat. Iberoam., 27 (1), pp. 181-232

Citas:

---------- APA ----------
Dickenstein, A. & Tabera, L.F. (2012) . Singular Tropical Hypersurfaces. Discrete and Computational Geometry, 47(2), 430-453.
http://dx.doi.org/10.1007/s00454-011-9364-6
---------- CHICAGO ----------
Dickenstein, A., Tabera, L.F. "Singular Tropical Hypersurfaces" . Discrete and Computational Geometry 47, no. 2 (2012) : 430-453.
http://dx.doi.org/10.1007/s00454-011-9364-6
---------- MLA ----------
Dickenstein, A., Tabera, L.F. "Singular Tropical Hypersurfaces" . Discrete and Computational Geometry, vol. 47, no. 2, 2012, pp. 430-453.
http://dx.doi.org/10.1007/s00454-011-9364-6
---------- VANCOUVER ----------
Dickenstein, A., Tabera, L.F. Singular Tropical Hypersurfaces. Discrete Comput. Geom. 2012;47(2):430-453.
http://dx.doi.org/10.1007/s00454-011-9364-6