The Bergman kernel in constant curvature
Alix Deleporte (IRMA)
TL;DR
This paper provides an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, with an exponentially small error term related to the inverse semiclassical parameter.
Contribution
It introduces a simplified proof method for the Bergman kernel approximation on homogeneous spaces, improving understanding of its asymptotic behavior.
Findings
Approximate Bergman kernel expression derived
Error term is exponentially small
Applicable to products of homogeneous spaces
Abstract
We present an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, and products of them. The error term is exponentially small with respect to the inverse semiclassical parameter.
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Taxonomy
TopicsGeometry and complex manifolds · Holomorphic and Operator Theory · Algebraic and Geometric Analysis