2023 / September Volume 18 No.3
Semi-classical asymptotics of Bergman and spectral kernels for $(0,q)$-forms
Published Date |
2023 / September
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Title | Semi-classical asymptotics of Bergman and spectral kernels for $(0,q)$-forms |
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Pagination | 299-364 |
Abstract | In this paper, we develop a new scaling method to study spectral and Bergman kernels for the k-th tensor power of a line bundle over a complex manifold under local spectral gap condition. In particular, we establish a simple proof of the pointwise asymptotics of spectral and Bergman kernels. As a new result, in the function case, we obtain the leading term of Bergman kernel under spectral gap with exponential decay. Moreover, in the general cases of $(0,q)$-forms, the asymptotics remain valid while the curvature of the line bundle is degenerate. |
DOI | |
AMS Subject Classification |
32L10
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Received |
2023-07-31
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Revised |
2023-11-06
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Accepted |
2023-11-06
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