Quantization of Abelian Varieties: distributional sections and the transition from K\"ahler to rea
Quantization of Abelian Varieties: distributional sections and the transition from K\"ahler to rea
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阿贝尔簇的量化：分布截面和从 K"ahler 到 rea 的转变
DOI：
10.1016/j.jfa.2010.01.023
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. P. Nunes
中科院分区：
文献类型：
--
作者：
Thomas Baier;J. Mourão;J. P. Nunes
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。真实的和混合极化被解释为简并的复杂结构。利用弱协变常数方程和描述分布截面的Weil-Brezin展开，给出了所有非负极化的量子化空间的统一解析描述.本文证明了不同极化情况下半形修正量子化空间之间的Blattner-Kostant-斯滕贝格（BKS）配对映射是传递的，并且与Sp（2g，R）的作用有关.此外，这些映射被证明是酉的。
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 non-negative 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.