  We study the parameter dependence of the Bergman kernels on some planar
domains depending on complex parameter \zeta in nontrivial "pseudoconvex" ways.
Smoothly bounded cases are studied at first: It turns out that, in an example
where the domains are annuli, the Levi form for the logarithm of the Bergman
kernels with respect to \zeta approaches to 0 as the point tends to the
boundary of the domain, and in another example where the domains are discs, it
approaches to 1 as the point tends to the complement of a point in the
boundary. Further, in contrast to this, in the cases where the boundary of the
domains are not smooth, such as discs with slits, rectangles and half strips,
completely different phenomena are observed.
