2016 / September Volume 11 No.3
The Second Coefficient of the Asymptotic Expansion of the Weighted Bergman Kernel for (0,q) Forms on $\mathbb{C^{n}}$
| Published Date |
2016 / September
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| Title | The Second Coefficient of the Asymptotic Expansion of the Weighted Bergman Kernel for (0,q) Forms on $\mathbb{C^{n}}$ |
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| Pagination | 521-570 |
| Abstract | Let $\phi\in C^\infty(\mathbb{C}^n)$ be a given real valued function. We assume that $\partial\bar\partial\phi$ is non-degenerate of constant signature $(n_-,n_+)$ on $\mathbb{C}^n$. When $q=n_-$, it is well-known that the Bergman kernel for $(0,q)$ forms with respect to the $k$-th weight $e^{-2k\phi}$, $k>0$, admits a full asymptotic expansion in $k$.
In this paper, we compute the trace of the second coefficient of the asymptotic expansion on the diagonal.
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| DOI | |
| AMS Subject Classification |
58J40, 32C15.
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| Received |
2016-08-07
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| Accepted |
2016-07-22
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