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Weakly special test configurations of log canonical Fano varieties

### Guodu Chen and Chuyu Zhou

Vol. 16 (2022), No. 10, 2415–2432
##### Abstract

Let $\left(X,\mathrm{\Delta }\right)$ be a strictly lc log Fano pair, we show that every lc place of complements of $\left(X,\mathrm{\Delta }\right)$ is dreamy and there exists a correspondence between weakly special test configurations of $\left(X,\mathrm{\Delta };-{K}_{X}-\mathrm{\Delta }\right)$ and lc places of complements of $\left(X,\mathrm{\Delta }\right)$.

##### Keywords
lc Fano variety, weakly special test configuration, complement
Primary: 14J17
Secondary: 14J45