BerezinToeplitz quantization on Khler manifolds

Xiaonan Ma 1  and George Marinescu 2
  • 1 Universit Paris DiderotParis 7, UFR de Mathmatiques, Case 7012, Site Chevaleret, 75205 Paris Cedex 13, France
  • 2 Universitt zu Kln, Mathematisches Institut, Weyertal 86-90, 50931 Kln, Germany Institute of Mathematics Simion Stoilow, Romanian Academy, Bucharest, Romania

Abstract

We study BerezinToeplitz quantization on Khler 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 BerezinToeplitz operators, and of the composition of two BerezinToeplitz operators. As an application, we estimate the norm of Donaldson's Q-operator.

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