Lattice point counting via Einstein metrics
Ziming Nikolas Ma, Naichung Conan Leung
TL;DR
This paper establishes a growth estimate for lattice points in Q-Gorenstein cones using advanced geometric and analytical tools, linking algebraic geometry, differential geometry, and orbifold theory.
Contribution
It introduces a novel approach combining Sasaki-Einstein metrics and orbifold index formulas to estimate lattice point counts in algebraic cones.
Findings
Derived a new growth estimate for lattice points in Q-Gorenstein cones.
Connected Sasaki-Einstein geometry with lattice point counting.
Applied Kawasaki-Riemann-Roch to orbifold settings.
Abstract
We obtain a growth estimate for the number of lattice points inside any Q-Gorenstein cone. Our proof uses the result of Futaki-Ono-Wang on Sasaki-Einstein metric for the toric Sasakian manifold associated to the cone, a Yau's inequality, and the Kawasaki-Riemann-Roch formula for orbifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory