An optimal gap of minimal log discrepancies of threefold non-canonical singularities

Abstract

We show that the minimal log discrepancy of any $\mathbb{Q}$-Gorenstein non-canonical threefold is $\le \frac{12}{13}$, which is an optimal bound.

24 pages. First revised version according to the referee. More details explained. Remove the algorithm tables (still can be found in version 1 on arXiv). Update the references

References in corpus (4)

• ACC for minimal log discrepancies of exceptional singularities
• Toward the equivalence of the ACC for $a$-log canonical thresholds and the ACC for minimal log discrepancies
• A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three
• Boundedness of $(\epsilon ,n)$-Complements for Surfaces

Cited by in corpus (3)

• Birational boundedness of rationally connected Calabi-Yau 3-folds
• Existence and boundedness of $n$-complements
• A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three