Integral Kahler Invariants and the Bergman kernel asymptotics for line bundles

On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed into a Chern polynomial (the integrand of a Chern number) and...

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Bibliographic Details
Published in:arXiv.org 2015-01
Main Authors: Alexakis, Spyros, Hirachi, Kengo
Format: Article
Language:English
Subjects:
Asymptotic series
Bundles
Curvature
Decomposition
Divergence
Integrals
Invariants
Kernels
Manifolds
Polynomials
Online Access:Get full text
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Summary:On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed into a Chern polynomial (the integrand of a Chern number) and divergences of one forms, which do not contribute to the integral. We apply this decomposition formula to describe the asymptotic expansion of the Bergman kernel for positive line bundles and to show that the CR Q-curvature on a Sasakian manifold is a divergence.
ISSN:2331-8422
DOI:10.48550/arxiv.1501.02463