Tsz On Mario Chan, Analytic Adjoint Ideal Sheaves via Residue Functions

In this talk, we introduce a modification of the analytic adjoint ideal sheaves. The original analytic adjoint ideal sheaves were studied by Guenancia and Dano Kim. The modified version makes use of the residue functions with respect to log-canonical (lc) measures, giving a sequence of adjoint ideal sheaves which provide a scheme-theoretic description of the lc centres of a given lc pair (X, S) (where X is a complex manifold) defined by multiplier ideal sheaves of quasi-psh functions with suitable regularity assumptions. We also discuss how the use of the residue functions helps to yield a local L² extension result without using the Ohsawa-Takegoshi extension theorem, and to provide residue L² norms on unions of lc centres which are invariant under any modifications of the ambient space X. Since some notions of singularities in birational geometry (namely, klt and lc) can be described via integrability conditions, the residue norms can be useful in the study of the inversion of adjunction.