Singular Projective Varieties and Quantization

Schlichenmaier, Martin

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URN: urn:nbn:de:bsz:180-madoc-16005
Document Type: Working paper
Year of publication: 2000
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Subject headings (SWD): Berezin-Transformation , Hilbert-Raum , Homogene Kähler-Mannigfaltigkeit
Abstract: By the quantization condition compact quantizable Kähler 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 geometrie 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 ecntribution 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 geometrie invariant theory are recalled.
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