Analytical Approximations and Monge–Ampère Masses of Plurisubharmonic Singularities

Abstract

Abstract We construct examples of plurisubharmonic functions with isolated singularities at $0\in {{\mathbb {C}}}^n$, whose residual Monge–Ampère masses at the origin cannot be approximated by masses of canonical analytic approximations obtained via multiplier ideals. This answers negatively a conjecture of Demailly, and shows that residual Monge–Ampère masses are not valuative invariants of plurisubharmonic singularities.