Resumen de The Van den Bergh duality and the modular symmetry of a Poisson variety

Vasiliy Dolgushev

• We consider a smooth Poisson affine variety with the trivial canon-ical bundle over C . For such a variety the deformation quantization algebra Aℏ obeys the conditions of the Van den Bergh duality theorem and the corresponding dualizing module is determined by an outer automorphism of Aℏ intrinsic to Aℏ . We show how this automorphism can be expressed in terms of the modular class of the corresponding Poisson variety. We also prove that the Van den Bergh dualizing module of the deformation quantization algebra Aℏ is free if and only if the corresponding Poisson structure is unimodular.