The number of vertices of a Fano polytope
classification
🧮 math.AG
math.CO
keywords
numberfanomaximalpolytopeverticesboundarycasescharacterize
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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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