Approximating delta invariants in the sense of complements of plt type

Abstract

In this note, we will show that delta invariant of a log Fano pair can be approximated by lc places of complements of plt type if it is no greater than one. Give a log Fano pair with delta invariant no greater than one, under the assumption that delta invariant of the log Fano pair can be approximated by lc places of bounded complements of plt type, we show the existence of the divisorial valuation computing delta invariant of this log Fano pair.