A New Definition of Analytic Adjoint Ideal Sheaves via the Residue Functions of Log-Canonical Measures I

A new definition of analytic adjoint ideal sheaves for quasi-plurisubharmonic (quasi-psh) functions with only neat singularities is studied and shown to admit some residue short exact sequences which are obtained by restricting sections the newly defined unions $\sigma$-log-canonical ($\sigma$-lc) centres. The induce naturally $L^2$ norms on $\sigma$-lc centres invariant under log-resolutions. They can also describe without need log-resolutions even if quasi-psh in question not a simple-normal-crossing configuration. This hinting their potential use discussing when have more general singularities. Furthermore, relations between algebraic Ein--Lazarsfeld as well those Hacon--McKernan described order illustrate role (potentially finer) measurement minimal model program. In course study, local extension theorem proven, shows that holomorphic any be extended holomorphically neighbourhood estimates. proof does rely techniques Ohsawa--Takegoshi-type theorems.