Berezin-Toeplitz quantization on Kaehler manifolds

Details Berezin-Toeplitz quantization on Kaehler manifolds Berezin-Toeplitz quantization on Kaehler manifolds

2010-09-22

arxiv.org/abs/1009.4405v3

J. Reine Angew. Math. 662 (2012), 1-56

Mathematics

Differential Geometry

45 pages, footnote at page 3 and Remark 0.5 added; v.3 is a final update to agree with the published paper

Scientific paper

We study the Berezin-Toeplitz quantization on Kaehler manifolds. We explain
first how to compute various associated asymptotic expansions, then we compute
explicitly the first terms of the expansion of the kernel of the
Berezin-Toeplitz operators, and of the composition of two Berezin-Toeplitz
operators. As application we estimate the norm of Donaldson's Q-operator.

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