Degeneration of log Calabi-Yau pairs via log canonical places

Abstract

Let $(X,\Delta )$ be a projective log canonical Calabi-Yau pair and $L$ an ample $\mathbb{Q}$-line bundle on $X$, we show that there is a correspondence between lc places of $(X,\Delta )$ and weakly special test configurations of $(X,\Delta ;L)$.

arXiv comment19 pages. Final version. Theorem 5.4 removed for further study. To appear in IMRN