ACC for Local-Volume-to-M minimal-Log-Discrepancy Ratios with DCC Coefficients

Determine whether the set of local-volume-to-minimal-log-discrepancy ratios for n-dimensional klt germs with boundary coefficients in a DCC set satisfies the ascending chain condition, for every integer n≥2 and every DCC set Γ⊆[0,1].

Background

The paper proves that, for fixed dimension and a finite coefficient set Γ, the ratios of local volumes to minimal log discrepancies form a set that is discrete away from zero and satisfies the ACC. It also recalls that local volumes satisfy the ACC for DCC coefficient sets. The unresolved question asks whether the ratio result extends from finite coefficient sets to arbitrary DCC coefficient sets, where the behavior of minimal log discrepancies and quotients may introduce additional accumulation phenomena.