Deformation quantization of a Kaehler-Poisson structure vanishing on a Levi nondegenerate hypersurface

TL;DR

This paper provides an elementary proof for the existence of a deformation quantization with separation of variables on complex manifolds with a Kaehler-Poisson structure that vanishes on a Levi nondegenerate hypersurface and is nondegenerate elsewhere.

Contribution

It offers a simplified proof of a known result regarding deformation quantization on specific complex manifolds with Kaehler-Poisson structures.

Findings

Existence of deformation quantization with separation of variables established

Elementary proof provided for a previously known result

Applicable to complex manifolds with Levi nondegenerate hypersurfaces

Abstract

We give an elementary proof of the result by Leichtnam, Tang, and Weinstein that there exists a deformation quantization with separation of variables on a complex manifold endowed with a Kaehler-Poisson structure vanishing on a Levi nondegenerate hypersurface and nondegenerate on its complement.