Types of quantum field thories
Hence the concept of Kähler polarization is that special case of polarization which connects most intimately the symplectic geometry to complex analytic geometry. The generalization of this from complex analytic geometry to more general algebraic geometry is the concept of a polarized algebraic variety.
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Discussion of the functoriality of Kähler polarization quantization with respect to the choice of metaplectically corrected Kähler structure is in section 3 of