Nondeformability of Moishezon manifolds with nonnegative Kodaira dimension

Abstract

Let $π:\X\to\D$ be a proper holomorphic submersion with connected fibers, and suppose that $X_t$ is biholomorphic to a fixed smooth Moishezon manifold $S$ for every $t\ne 0$. If $\kappa (S)\ge 0$, we prove that $X_0\simeq S$.