The quantization of a toric manifold is given by the integer lattice points in the moment polytope

TL;DR

This paper explains how the quantization space dimension of a toric manifold, with a Kaehler polarization, equals the count of integer lattice points in its moment polytope, linking geometric and combinatorial data.

Contribution

It provides a clear argument connecting the quantization dimension to lattice points in the moment polytope, clarifying a key aspect of geometric quantization for toric manifolds.

Findings

Dimension of quantization space equals lattice point count

Establishes a direct link between geometry and combinatorics

Simplifies understanding of quantization in toric manifolds

Abstract

We describe a very nice argument, which we learned from Sue Tolman, that the dimension of the quantization space of a toric manifold, using a Kaehler polarization, is given by the number of integer lattice points in the moment polytope.