Moderate Degeneration of Kähler–Einstein Manifolds with Negative Ricci Curvature

Abstract

We study a family of Kähler–Einstein manifolds with negative Ricci curvature over a curve with a possibly singular special fiber. We show that if the diameters of the smooth fibers are uniformly bounded, then the special fiber has log-terminal singularities at worst after a finite base change and a birational modification.