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

TL;DR

This paper establishes the precise upper bound for the minimal log discrepancy of non-canonical threefold singularities, advancing understanding in algebraic geometry.

Contribution

It proves the optimal upper bound of 12/13 for minimal log discrepancies of non-canonical threefolds, a key invariant in singularity theory.

Findings

Minimal log discrepancy of non-canonical threefolds is at most 12/13.

The bound of 12/13 is proven to be optimal.

Provides a definitive limit for singularity severity in threefolds.

Abstract

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