Twisted Deformation Quantization of Algebraic Varieties

Details Twisted Deformation Quantization of Algebraic Varieties Twisted Deformation Quantization of Algebraic Varieties

2009-05-04

arxiv.org/abs/0905.0488v3

Mathematics

Algebraic Geometry

AMSLaTeX, 62 pages, 3 ps figures. Numerous small improvements. Version 3: major rewrite, in content and organization. Replaced

Scientific paper

Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf of X. These are stack-like versions of usual deformations. We prove that there is a twisted quantization map from twisted Poisson deformations to twisted associative deformations, which is canonical and bijective on gauge equivalence classes. This result extends work of Kontsevich, and our own earlier work, on deformation quantization of algebraic varieties.

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