2000/05/31 by Martin Schlichenmaier, Schlichenmaier, Martin
Mathematics · Physics and Astronomy · #14A22 #53C55 #58F05 #58F06 #81S10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Symplectic Geometry (math.SG) #Tensor decomposition and applications #math-ph #math.AG #math.CV #math.DG #math.MP #math.QA #math.SG #msc:14A22 #msc:53C55 #msc:58F05 #msc:58F06 #msc:81S10 #quant-ph
paper · pdf · doi:10.48550/arxiv.math/0005288
21 pages, 3 figures
arxiv created 2000/05/31 · openalex publication_date 2000/05/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric quantization) is the projective coordinate ring of the embedded manifold. This allows for generalization to the case of singular varieties. The set-up is explained in the first part of the contribution. The second part of the contribution is of tutorial nature. Necessary notions, concepts, and results of algebraic geometry appearing in this approach to quantization are explained. In particular, the notions of projective varieties, embeddings, singularities, and quotients appearing in geometric invariant theory are recalled.