On the asymptotic expansion of Bergman kernel
Xianzhe Dai, Kefeng Liu, Xiaonan Ma
TL;DR
This paper investigates the asymptotic behavior of the Bergman kernel associated with the spin$^c$ Dirac operator on high tensor powers of a line bundle, providing insights into its expansion properties.
Contribution
It offers a detailed analysis of the asymptotic expansion of the Bergman kernel for the spin$^c$ Dirac operator, advancing understanding in complex geometry and analysis.
Findings
Derived explicit asymptotic expansion formulas
Identified leading order terms in the expansion
Enhanced understanding of geometric quantization processes
Abstract
We study the asymptotic of the Bergman kernel of the spin Dirac operator on high tensor powers of a line bundle.
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Taxonomy
TopicsGeometry and complex manifolds · Holomorphic and Operator Theory · Geometric Analysis and Curvature Flows