The number of vertices of a Fano polytope
[Le nombre de sommets d’un polytope de Fano]
Casagrande, Cinzia
Annales de l'Institut Fourier, Tome 56 (2006), p. 121-130 / Harvested from Numdam
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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.

Publié le : 2006-01-01
DOI : https://doi.org/10.5802/aif.2175
Classification:  52B20,  14M25,  14J45
Mots clés: variétés toriques, variétés de Fano, polytopes réflexifs, polytopes de Fano 
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     title = {The number of vertices of a Fano polytope},
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     year = {2006},
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     doi = {10.5802/aif.2175},
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Casagrande, Cinzia. The number of vertices of a Fano polytope. Annales de l'Institut Fourier, Tome 56 (2006) pp. 121-130. doi : 10.5802/aif.2175. http://gdmltest.u-ga.fr/item/AIF_2006__56_1_121_0/

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