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Volume and lattice points of reflexive simplices

Benjamin Nill
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Abstract

We prove sharp upper bounds on the volume and the number of lattice points on edges of higher-dimensional reflexive simplices. These convex-geometric results are derived from new number-theoretic bounds on the denominators of unit fractions summing up to one. The main algebro-geometric application is a sharp upper bound on the anticanonical degree of higher-dimensional Q-factorial Gorenstein toric Fano varieties with Picard number one, where we completely characterize the case of equality.

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Benjamin Nill. 2007-01-15. Volume and lattice points of reflexive simplices. https://doi.org/10.1007/s00454-006-1299-y

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