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Abstract:

We present a formula for the degree of the discriminant of a smooth projective toric variety associated to a lattice polytope P, in terms of the number of integral points in the interior of dilates of faces of dimension greater or equal than {top left corner}dimP/2{top right corner}. © 2012.

Registro:

Documento: Artículo
Título:A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes
Autor:Dickenstein, A.; Nill, B.; Vergne, M.
Filiación:Departamento de Matemática, FCEN, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pab I, (C1428EGA) Buenos Aires, Argentina
Case Western Reserve University, Department of Mathematics, 10900, Euclid Avenue, Cleveland, OH 44106, United States
Institut de mathématiques de Jussieu, 175, rue du Chevaleret, 75013 Paris, France
Año:2012
Volumen:350
Número:5-6
Página de inicio:229
Página de fin:233
DOI: http://dx.doi.org/10.1016/j.crma.2012.02.001
Título revista:Comptes Rendus Mathematique
Título revista abreviado:C. R. Math.
ISSN:1631073X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1631073X_v350_n5-6_p229_Dickenstein

Referencias:

  • Batyrev, V.V., Nill, B., Multiples of lattice polytopes without interior lattice points (2007) Mosc. Math. J., 7, pp. 195-207
  • Beck, M., Robins, S., Computing the Continuous Discretely: Integer Point Enumeration in Polyhedra (2007) Undergraduate Texts in Mathematics, , Springer-Verlag
  • Brion, M., Points entiers dans les polyèdres convexes (1988) Ann. Sci. Ecole Norm. Sup., 21, pp. 653-663
  • Di Rocco, S., Projective duality of toric manifolds and defect polytopes (2006) Proc. London Math. Soc., 93, pp. 85-104
  • Dickenstein, A., Nill, B., A simple combinatorial criterion for projective toric manifolds with dual defect (2010) Math. Res. Lett., 17 (3), pp. 435-448
  • Ehrhart, E., PolynÔmes arithmétiques et méthode des polyèdres en combinatoire (1977) International Series of Numerical Mathematics, 35. , Birkhäuser Verlag
  • Gel'fand, I., Kapranov, M., Zelevinsky, A., (1994) Discriminants, Resultants and Multidimensional Determinants, , Birkhäuser, Boston
  • Haase, C., Nill, B., Payne, S., Cayley decompositions of lattice polytopes and upper bounds for h *-polynomials (2009) J. Reine Angew. Math., 637, pp. 207-216
  • Hegedüs, G., Kasprzyk, A.M., The boundary volume of a lattice polytope, , preprint, arxiv:1002.2815
  • Novelli, J.C., Thibon, J.Y., Non-commutative symmetric functions and an amazing matrix, , preprint, arxiv:1109.1184
  • Stanley, R.P., A monotonicity property of h-vectors and h *-vectors (1993) Eur. J. Comb., 14, pp. 251-258
  • Ziegler, G., Lectures on Polytopes (1995) Graduate Texts in Mathematics, 152. , Springer-Verlag

Citas:

---------- APA ----------
Dickenstein, A., Nill, B. & Vergne, M. (2012) . A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes. Comptes Rendus Mathematique, 350(5-6), 229-233.
http://dx.doi.org/10.1016/j.crma.2012.02.001
---------- CHICAGO ----------
Dickenstein, A., Nill, B., Vergne, M. "A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes" . Comptes Rendus Mathematique 350, no. 5-6 (2012) : 229-233.
http://dx.doi.org/10.1016/j.crma.2012.02.001
---------- MLA ----------
Dickenstein, A., Nill, B., Vergne, M. "A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes" . Comptes Rendus Mathematique, vol. 350, no. 5-6, 2012, pp. 229-233.
http://dx.doi.org/10.1016/j.crma.2012.02.001
---------- VANCOUVER ----------
Dickenstein, A., Nill, B., Vergne, M. A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes. C. R. Math. 2012;350(5-6):229-233.
http://dx.doi.org/10.1016/j.crma.2012.02.001