In this paper we study the microlocal properties of the Szegő kernel of a given compact connected orientable CR orbifold, whose Kohn Laplacian has closed range. This last assumption is satisfied if certain geometric conditions hold true, as in the smooth case. Furthermore, we explain how to generalize a CR version of quantization commutes with reduction to orbifolds. As an application, we give a pure analytic proof of Kodaira-Bailey theorem.
Galasso, A., Hsiao, C. (2025). On the singularities of the Szegő kernels on CR orbifolds. JOURNAL OF GEOMETRY AND PHYSICS, 209(March 2025) [10.1016/j.geomphys.2024.105411].
On the singularities of the Szegő kernels on CR orbifolds
Galasso, A
;
2025
Abstract
In this paper we study the microlocal properties of the Szegő kernel of a given compact connected orientable CR orbifold, whose Kohn Laplacian has closed range. This last assumption is satisfied if certain geometric conditions hold true, as in the smooth case. Furthermore, we explain how to generalize a CR version of quantization commutes with reduction to orbifolds. As an application, we give a pure analytic proof of Kodaira-Bailey theorem.
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