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The number of vertices of a Fano polytope

C. Casagrande
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Abstract

Let X be a complex, 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.

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C. Casagrande. 2005-11-15. The number of vertices of a Fano polytope. https://arxiv.org/abs/math/0411073

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