The second coefficient of the asymptotic expansion of the weighted Bergman kernel for (0,q) forms on $\Complex^n$
Abstract
Let $\phi\in C^\infty(\Complex^n)$ be a given real valued function. We assume that $\pr\ddbar\phi$ is non-degenerate of constant signature
(
n
−
,
n
+
)
on $\Complex^n$. When
q=
n
−
, it is well-known that the Bergman kernel for
(0,q)
forms with respect to the
k
-th weight
e
−2kϕ
,
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.