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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.02548 |
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Table of Contents:
- This paper presents a simple method to prove the heat kernel asymptotics for the Kodaira Laplacian with respect to the high power of a holomorphic Hermitian line bundle $(L,h^L)$ over a possibly non-compact Hermitian manifold $(M,ω)$. As a consequence, we give a direct proof of the holomorphic Morse inequalities on covering manifolds. Furthermore, we generalize it to the vector bundle via the $L^2$ Le Potier isomorphism and provide an algebraic version of the holomorphic Morse inequalities. The approach used in this work employs a scaling technique and is applicable to $M$ regardless of its compactness.