Divisors computing minimal log discrepancies on lc surfaces

Abstract

AbstractLet$(X\ni x,B)$be an lc surface germ. If$X\ni x$is klt, we show that there exists a divisor computing the minimal log discrepancy of$(X\ni x,B)$that is a Kollár component of$X\ni x$. If$B\not=0$or$X\ni x$is not Du Val, we show that any divisor computing the minimal log discrepancy of$(X\ni x,B)$is a potential lc place of$X\ni x$. This extends a result of Blum and Kawakita who independently showed that any divisor computing the minimal log discrepancy on a smooth surface is a potential lc place.