%0 Journal Article
%T Quantization of Abelian Varieties: distributional sections and the transition from K£¿hler to real polarizations
%A Thomas Baier
%A Jos¨¦ M. Mour£¿o
%A Jo£¿o P. Nunes
%J Mathematics
%D 2009
%I arXiv
%X We study the dependence of geometric quantization of the standard symplectic torus on the choice of invariant polarization. Real and mixed polarizations are interpreted as degenerate complex structures. Using a weak version of the equations of covariant constancy, and the Weil-Brezin expansion to describe distributional sections, we give a unified analytical description of the quantization spaces for all nonnegative polarizations. The Blattner-Kostant-Sternberg (BKS) pairing maps between half-form corrected quantization spaces for different polarizations are shown to be transitive and related to an action of $Sp(2g,\R)$. Moreover, these maps are shown to be unitary.
%U http://arxiv.org/abs/0907.5324v3