Toward an inductive description of singularities of pairs

TL;DR

This paper introduces an inductive approach to understanding singularities of pairs, linking the log canonicity in higher dimensions to that in lower dimensions, motivated by Shokurov's ACC Conjecture.

Contribution

It provides a new inductive characterization of log canonicity for pairs on smooth varieties, advancing the theoretical understanding of singularities.

Findings

Characterizes log canonicity in dimension N+1 via lower-dimensional pairs

Establishes a framework connecting singularities across dimensions

Supports the study of Shokurov's ACC Conjecture for log canonical thresholds

Abstract

Motivated by Shokurov's ACC Conjecture for log canonical thresholds, we propose an inductive point of view on singularities of pairs, in the case when the ambient variety is smooth. Our main result characterizes the log canonicity of a pair in dimension N+1 by the log canonicity of another pair (not effective, in general) in dimension N.