Non-rational centers of log canonical singularities

TL;DR

This paper establishes a connection between the dimensions of non-klt centers in log canonical pairs and the depth of the variety at closed points, providing new insights into the structure of singularities.

Contribution

It proves that log canonical pairs with certain dimension conditions on non-klt centers have depth at least d+2 at all closed points, linking singularity types to depth properties.

Findings

Depth of X is at least d+2 at every closed point.

Non-klt centers of dimension at least d influence the depth of the variety.

Provides a criterion relating singularity centers to depth in algebraic geometry.

Abstract

We show that if $(X,B)$ is a log canonical pair with $\dim X\geq d+2$, whose non-klt centers have dimension $\geq d$, then $X$ is has depth $\ge d+2$ at every closed point.