Sources of log canonical centers

Abstract

Given a log canonical pair $(X,\Delta)$ and a log canonical center $Z\subset X$, we define a Calabi–Yau fiber space $(S,\Delta_S)\to Z$, called the source of $Z$. We believe that the source carries – and makes accessible – all the relevant information about the log canonical center $Z$. There is a natural Poincaré residue map from $X$ to $S$ which is used to solve several problems in higher-codimension adjunction. The main application is to the construction of semi-log-canonical pairs.