阿贝尔簇的量子化：分布截面和从Kähler到实极化的转变
Quantization of Abelian Varieties: distributional sections and the transition from Kähler to real polarizations
摘要：
我们研究了标准辛环面的几何量子化对不变极化选择的依赖性。实极化和混合极化被解释为简并复结构。利用协变常数方程的弱形式和描述分布截面的Weil-Brezin展开，给出了所有非负极化量子化空间的统一解析描述. Blattner-Kostant-Sternberg（BKS）配对映射之间的半形校正的量子化空间为不同的极化被证明是可传递的，并与$Sp(2g,\R)$的作用。此外，这些地图被证明是酉的。
英文摘要：
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.
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