Volume and lattice points of reflexive simplices

Details Volume and lattice points of reflexive simplices Volume and lattice points of reflexive simplices

2004-12-23

arxiv.org/abs/math/0412480v3

Discr. Comp. Geom. 37 (2007), 301-320

Mathematics

Algebraic Geometry

AMS-LaTeX, 19 pages; paper reorganized, introduction added, bibliography updated; typos corrected

Scientific paper

10.1007/s00454-006-1299-y

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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