Second-Largest Ratio for Boundary-Free Klt Germs

Determine whether, for every integer n≥2, the second-largest value of the set of local-volume-to-minimal-log-discrepancy ratios of n-dimensional klt germs with zero boundary is respectively 4/3 for n=2, 2(n−1)^(n−1) for n=3 or 4, and n^n/(n+1) for n≥5.

Background

The paper establishes that the ratio set with zero boundary is discrete away from zero and therefore has a second-largest value. It then proposes an explicit dimension-dependent formula for that value. The proposed values are not proved in the paper and are presented as an unresolved question concerning the fine structure of the ratio set beyond its largest element.