Navegar

Colección

Datos Estadísticas

Artículo

Cattani, E.; Cueto, M.A.; Dickenstein, A.; Di Rocco, S.; Sturmfels, B. "Mixed discriminants" (2013) Mathematische Zeitschrift. 274(3-4):761-778
La versión final de este artículo es de uso interno de la institución.
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plücker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves. © 2012 Springer-Verlag Berlin Heidelberg.

Registro:

Documento: Artículo
Título:Mixed discriminants
Autor:Cattani, E.; Cueto, M.A.; Dickenstein, A.; Di Rocco, S.; Sturmfels, B.
Filiación:Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003, United States
FB12 Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Str. 6-8, 60325 Frankfurt am Main, Germany
Departamento de Matemática, FCEN, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pab, I - C1428EGA, Buenos Aires, Argentina
KTH, Mathematics, S-10044 Stockholm, Sweden
Department of Mathematics, University of California, Berkeley, CA, 94720, United States
Palabras clave:A-discriminant; Cayley polytope; Degree; Matroid strata; Mixed Grassmannian; Multiple root; Tropical discriminant
Año:2013
Volumen:274
Número:3-4
Página de inicio:761
Página de fin:778
DOI: http://dx.doi.org/10.1007/s00209-012-1095-8
Título revista:Mathematische Zeitschrift
Título revista abreviado:Math. Z.
ISSN:00255874
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255874_v274_n3-4_p761_Cattani

Referencias:

  • Ardila, F., Klivans, C.J., The Bergman complex of a matroid and phylogenetic trees (2006) J. Combin. Theory Ser. B, 96 (1), pp. 38-49
  • Benoist, O., Degrés d'homogénéité de l'ensemble des intersections complètes singulières (2012) Annales de l'Institut Fourier, 62 (3), pp. 1189-1214
  • Bernstein, D.N., The number of roots of a system of equations (1975) Funkcional Anal. I Prilož., 9 (3), pp. 1-4
  • Casagrande, C., Di Rocco, S., Projective ℚQ-factorial toric varieties covered by lines (2008) Commun. Contemp. Math., 10 (3), pp. 363-389
  • Cattani, E., Dickenstein, A., Sturmfels, B., Rational hypergeometric functions (2001) Compositio Math., 128 (2), pp. 217-239
  • Curran, R., Cattani, E., Restriction of A-discriminants and dual defect toric varieties (2007) J. Symb. Comput., 42 (1-2), pp. 115-135
  • Dickenstein, A., Feichtner, E.M., Sturmfels, B., Tropical discriminants (2007) J. Am. Math. Soc, 20 (4), pp. 1111-1133
  • Dickenstein, A., Sturmfels, B., Elimination theory in codimension 2 (2002) J. Symb. Comput., 34 (2), pp. 119-135
  • Di Rocco, S., Projective duality of toric manifolds and defect polytopes (2006) Proc. London Math. Soc. (3), 93 (1), pp. 85-104
  • Esterov, A., Newton polyhedra of discriminants of projections (2010) Discret. Comput. Geom., 44 (1), pp. 96-148
  • Feichtner, E.M., Sturmfels, B., Matroid polytopes, nested sets and Bergman fans (2005) Port. Math, 62 (4), pp. 437-468. , (N. S.)
  • GelGel′fand, I.M., Kapranov, M.M., Zelevinsky, A.V., Discriminants, resultants, and multidimensional determinants (1994) Mathematics: Theory & Applications. Birkhäuser Boston Inc, , Boston
  • Katz, N., Pinceaux de Lefschetz: Théoréme d'existence (1973) Exposé XVII in Groupes de Monodromie en Géométrie Algébrique, 340, pp. 212-253. , (SGA 7 II). In: Lecturer Notes in Mathematics,Springer, Berlin
  • Matsui, Y., Takeuchi, K., A geometric degree formula for A-discriminants and Euler obstructions of toric varieties (2011) Adv. Math, 226 (2), pp. 2040-2064
  • Nie, J., Discriminants and non-negative polynomials (2012) J. Symb. Comput., 47, pp. 167-191
  • Rincón, E.F., Computing tropical linear spaces (2012) J. Symb. Comput, , (in press)
  • Salmon, G., A treatise on the higher plane curves: intended as a sequel to "A treatise on conic sections", 3rd edn (1852) Hodges and Smith, , Dublin
  • Shub, M., Smale, S., Complexity of Bézout's theorem. I. Geometric aspects (1993) J. Am. Math. Soc., 6 (2), pp. 459-501

Citas:

---------- APA ----------
Cattani, E., Cueto, M.A., Dickenstein, A., Di Rocco, S. & Sturmfels, B. (2013) . Mixed discriminants. Mathematische Zeitschrift, 274(3-4), 761-778.
http://dx.doi.org/10.1007/s00209-012-1095-8
---------- CHICAGO ----------
Cattani, E., Cueto, M.A., Dickenstein, A., Di Rocco, S., Sturmfels, B. "Mixed discriminants" . Mathematische Zeitschrift 274, no. 3-4 (2013) : 761-778.
http://dx.doi.org/10.1007/s00209-012-1095-8
---------- MLA ----------
Cattani, E., Cueto, M.A., Dickenstein, A., Di Rocco, S., Sturmfels, B. "Mixed discriminants" . Mathematische Zeitschrift, vol. 274, no. 3-4, 2013, pp. 761-778.
http://dx.doi.org/10.1007/s00209-012-1095-8
---------- VANCOUVER ----------
Cattani, E., Cueto, M.A., Dickenstein, A., Di Rocco, S., Sturmfels, B. Mixed discriminants. Math. Z. 2013;274(3-4):761-778.
http://dx.doi.org/10.1007/s00209-012-1095-8