Benjamin Nill
Published 2004-12-23, updated 2007-01-15Version 3
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.
Comments: AMS-LaTeX, 19 pages; paper reorganized, introduction added, bibliography updated; typos corrected
Journal: Discr. Comp. Geom. 37 (2007), 301-320
Q-factorial Gorenstein toric Fano varieties with large Picard number
Few smooth d-polytopes with n lattice points
Sharp bounds on fake weighted projective spaces with canonical singularities
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