Degeneration of log Calabi-Yau pairs via log canonical places

TL;DR

This paper establishes a correspondence between log canonical places of a projective log canonical Calabi-Yau pair and weakly special test configurations of the pair with an ample line bundle, advancing understanding of degenerations in algebraic geometry.

Contribution

It introduces a novel link between lc places and weakly special test configurations in the context of Calabi-Yau pairs, providing new tools for studying degenerations.

Findings

Established a correspondence between lc places and test configurations.

Connected geometric singularities with algebraic degenerations.

Enhanced methods for analyzing Calabi-Yau degenerations.

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 $(X, \Delta;L)$.