The number of vertices of a Fano polytope

Details The number of vertices of a Fano polytope The number of vertices of a Fano polytope

2004-11-03

arxiv.org/abs/math/0411073v3

Mathematics

Algebraic Geometry

Final version, to appear in Annales de l'Institut Fourier

Scientific paper

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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