Comptes Rendus
Combinatorics
A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes
[Une relation entre nombre de points entiers, volumes des faces et degré du discriminant des polytopes entiers non singuliers]
Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 229-233.

Nous donnons une formule pour le degré du discriminant dʼune variété torique projective non singulière associée à un polytope entier P, en terme du nombre de points entiers des intérieurs de dilatations de faces de dimension supérieure ou égale à dimP2.

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 dimP2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.02.001

Alicia Dickenstein 1 ; Benjamin Nill 2 ; Michèle Vergne 3

1 Departamento de Matemática, FCEN, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pab I, (C1428EGA) Buenos Aires, Argentina
2 Case Western Reserve University, Department of Mathematics, 10900, Euclid Avenue, Cleveland, OH 44106, USA
3 Institut de mathématiques de Jussieu, 175, rue du Chevaleret, 75013 Paris, France
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Alicia Dickenstein; Benjamin Nill; Michèle Vergne. A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes. Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 229-233. doi : 10.1016/j.crma.2012.02.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.02.001/

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