ON BOUNDEDNESS OF DIVISORS COMPUTING MINIMAL LOG DISCREPANCIES FOR SURFACES

Abstract Let $\Gamma $ be a finite set, and $X\ni x$ fixed kawamata log terminal germ. For any lc germ $(X\ni x,B:=\sum _{i} b_iB_i)$ , such that $b_i\in \Gamma Nakamura’s conjecture, which is equivalent to the ascending chain condition conjecture for minimal discrepancies germs, predicts there always exists prime divisor E over $a(E,X,B)=\mathrm {mld}(X\ni x,B)$ $a(E,X,0)$ bounded from above. We extend setting not necessarily satisfies descending condition, show it holds surfaces. also find some sufficient conditions boundedness of .