The number of vertices of a Fano polytope
[Le nombre de sommets d’un polytope de Fano]
Casagrande, Cinzia1
1 Università di Pisa Dipartimento di Matematica “L. Tonelli” Largo Bruno Pontecorvo, 5 56127 Pisa (Italy)
Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 121-130.

Soit X une variété de Fano torique, Gorenstein et ℚ-factorielle. Nous démontrons deux conjectures sur le nombre de Picard maximal de X en fonction de sa dimension et de son pseudo-indice, et nous caractérisons les cas limites. De façon équivalente, nous déterminons le nombre maximal de sommets d’un polytope réflexif simplicial.

Let X be a Gorenstein, ℚ-factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of X in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.

DOI : 10.5802/aif.2175
Classification : 52B20, 14M25, 14J45
Keywords: toric varieties, Fano varieties, reflexive polytopes, Fano polytopes
Mot clés : variétés toriques, variétés de Fano, polytopes réflexifs, polytopes de Fano
Casagrande, Cinzia 1

1 Università di Pisa Dipartimento di Matematica “L. Tonelli” Largo Bruno Pontecorvo, 5 56127 Pisa (Italy) 
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Casagrande, Cinzia. The number of vertices of a Fano polytope. Annales de l'Institut Fourier, Tome 56 (2006) no. 1, pp. 121-130. doi : 10.5802/aif.2175. https://www.numdam.org/articles/10.5802/aif.2175/

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