Abstract
In this paper we prove the following main result. Let D be a smoothly bounded pseudoconvex domain in C n with n ≥ 1. Suppose that there exists a complex variety sitting in the boundary bD; then we have K D (z, w) ∉ C ∞ (D̄ × D̄ - Δ(bD)). In particular, the Bergman kernel function associated with the Diederich-Fornaess worm domain is not smooth up to the boundary in joint variables off the diagonal of the boundary. © 1996 American Mathematical Society.