Weakly special test configurations of log canonical Fano varieties

TL;DR

This paper establishes a correspondence between weakly special test configurations and lc places of complements for strictly log canonical Fano varieties, providing new insights into their geometric structure.

Contribution

It proves that all lc places of complements are dreamy and links weakly special test configurations to these lc places in log canonical Fano varieties.

Findings

All lc places of complements are dreamy.

A correspondence exists between weakly special test configurations and lc places of complements.

Provides new structural understanding of log canonical Fano varieties.

Abstract

Let $X$ be a strictly log canonical Fano variety, we show that every lc place of complements is dreamy, and there exists a correspondence between weakly special test configurations of $(X,-K_X)$ and lc places of complements.