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Lattice points counting via Einstein metrics. (English) Zbl 1267.53047

The authors obtain a growth estimate for the number of lattice points inside any \(\mathbb Q\)-Gorenstein cone. The proof uses the result of Futaki-Ono-Wang on Sasaki-Einstein metric for the toric Sasakian manifold associated to the cone, a Yau inequality, and the Kawasaki-Riemann-Roch formula for orbifolds.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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