Toward the equivalence of the ACC for $a$-log canonical thresholds and the ACC for minimal log discrepancies

Abstract

In this paper, we show that Shokurov's conjectures on the ACC for $a$-lc thresholds and the ACC for minimal log discrepancies are equivalent in the interval $[0,1)$. That is, the conjecture on ACC for $a$-lc thresholds holds for every $0\le a<1$ if and only if the set of minimal log discrepancies for pairs with DCC coefficients do not have an accumulation point from below which belongs to $[0,1)$.

23p, version 3. comments are welcome. Proof of the main theorem greatly simplified. Section 3 added. Some results (Theorem 1.7) strengthened

References in corpus (2)

• ACC for minimal log discrepancies of exceptional singularities
• A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three

Cited by in corpus (6)

• ACC for minimal log discrepancies of exceptional singularities
• Birational boundedness of rationally connected Calabi-Yau 3-folds
• A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three
• Boundedness of $(\epsilon ,n)$-Complements for Surfaces
• An optimal gap of minimal log discrepancies of threefold non-canonical singularities
• Rational nef and anti-nef polytopes are not uniform