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

2007/08/21 by Mark Hamilton, Mark D. Hamilton, Hamilton, Mark D.
Mathematics · #53D50 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D50

paper · pdf · doi:10.48550/arxiv.0708.2710

10 pages, LaTeX, 3 figures; v2 minor changes: some small clarifications added, typos fixed. To appear in proceedings of 2006 International Toric Topology Conference

openalex publication_date 2007/08/21 · arxiv created 2008/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Locally toric manifolds and singular Bohr-Sommerfeld leaves
• Complex symplectomorphisms and pseudo-K "ahler islands in the\n quantization of toric manifolds
• Bohr-Sommerfeld quantization of b-symplectic toric manifolds
• A new look at unitarity in quantization commutes with reduction for toric manifolds
• A weighted version of quantization commutes with reduction for a toric manifold