Nadel-type multiplier ideal sheaves on complex spaces with singularities

In this article, we introduce multiplier ideal sheaves on complex spaces with singularities (not necessarily normal) via Ohsawa’s extension measure, as a special case of which, it turns out to be the so-called Mather-Jacobian multiplier ideals in the algebro-geometric setting. Inspired by Nadel’s coherence and Guan-Zhou’s strong openness properties of the multiplier ideal sheaves, we discuss similar properties for the generalized multiplier ideal sheaves. As applications, we obtain a reasonable generalization of (algebraic) adjoint ideal sheaves to the analytic setting and establish some extension theorems on Kähler manifolds from singular hypersurfaces. Relying on our multiplier and adjoint ideals, we also give characterizations for several important classes of singularities of pairs associated with plurisubharmonic functions.