Infinitesimal structure of log canonical thresholds

Abstract

We show that log canonical thresholds of fixed dimension are standardized. More precisely, we show that any sequence of log canonical thresholds in fixed dimension $d$ accumulates either (i) in a way which is similar to how standard and hyperstandard sets accumulate, or (ii) to log canonical thresholds in dimension $\le d-2$. This provides an accurate description on the infinitesimal structure of the set of log canonical thresholds. We also discuss similar behaviors of minimal log discrepancies, canonical thresholds, and K-semistable thresholds.