Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties

TL;DR

This paper proves Shokurov's ACC conjecture for log canonical thresholds on smooth, locally complete intersection, and quotient singularity varieties, confirming the ascending chain condition in these cases.

Contribution

It establishes the validity of Shokurov's ACC conjecture for a broad class of varieties, including smooth and certain singular varieties.

Findings

Proves ACC conjecture for smooth varieties

Extends proof to locally complete intersection varieties

Includes varieties with quotient singularities

Abstract

Shokurov conjectured that the set of all log canonical thresholds on varieties of bounded dimension satisfies the ascending chain condition. In this paper we prove that the conjecture holds for log canonical thresholds on smooth varieties and, more generally, on locally complete intersection varieties and on varieties with quotient singularities.