no. 5-6
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]
Présenté par : Claire Voisin
Dickenstein, Alicia1 ; Nill, Benjamin2 ; Vergne, Michèle3
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
Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 229-233

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⌉.

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⌉.

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

Dickenstein, Alicia 1 ; Nill, Benjamin 2 ; Vergne, Michèle 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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     title = {A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes},
     journal = {Comptes Rendus. Math\'ematique},
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Dickenstein, Alicia; Nill, Benjamin; Vergne, Michèle. A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes. Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 229-233. doi: 10.1016/j.crma.2012.02.001

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