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 ≤ 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.
No takes yet. Share an insight, caveat, or question.
Liu et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: