A GEOMETRIC CHARACTERIZATION OF A SIMPLE K3-SINGULARITY

Abstract

A simple K3-singularity is a three-dimensional normal isolated singularity with a certain condition on the mixed Hodge structure on a good resolution. We prove here that a three-dimensional normal isolated singularity is a simple K3-singularity if and only if the exceptional divisor of a Q-factorial terminal modification is an irreducible normal K3-surface.