The number of vertices of a Fano polytope
Annales de l'Institut Fourier, Volume 56 (2006) no. 1, p. 121-130

Let X be a Gorenstein, -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.

Soit X une variété de Fano torique, Gorenstein et -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.

DOI : https://doi.org/10.5802/aif.2175
Classification:  52B20,  14M25,  14J45
Keywords: toric varieties, Fano varieties, reflexive polytopes, Fano polytopes
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     author = {Casagrande, Cinzia},
     title = {The number of vertices of a Fano polytope},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {1},
     year = {2006},
     pages = {121-130},
     doi = {10.5802/aif.2175},
     mrnumber = {2228683},
     zbl = {1095.52005},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2006__56_1_121_0}
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Casagrande, Cinzia. The number of vertices of a Fano polytope. Annales de l'Institut Fourier, Volume 56 (2006) no. 1, pp. 121-130. doi : 10.5802/aif.2175. http://www.numdam.org/item/AIF_2006__56_1_121_0/

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