The second coefficient of the asymptotic expansion of the weighted Bergman kernel for $(0,q)$ forms on ${\mathbb{C}}^n$

Abstract

Let $\varphi \in C^{\infty }({\mathbb{C}}^n)$ be a given real valued function. We assume that $\pr\ddbarϕ$ 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 $e^{-2k\varphi }$, $k>0$, 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.

arXiv comment54 pages

References in corpus (1)

• Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles

Cited by in corpus (4)

• Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles
• The second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator
• On the second coefficient of the asymptotic expansion of Boutet de Monvel--Sjöstrand
• On the coefficients of the equivariant Szegő kernel asymptotic expansions