论文标题
关于除数的界限，计算表面的最小日志差异
On boundedness of divisors computing minimal log discrepancies for surfaces
论文作者
论文摘要
令$γ$为有限的集合，$ x \ ni x $固定的klt胚芽。对于任何lc grem $（x \ ni x，b：= \ sum_ {i} b_ib_i）$ $ a（e，x，b）= {\ rm {mld}}（x \ ni x，b）$和$ a（e，x，0）$的$从上方界定。我们将Nakamura的猜想扩展到了$ x \ ni x $不一定固定的，并且$γ$满足DCC，并表明其对表面的保留。对于任何此类$ e $，我们还为$ a（e，x，0）$的有限性找到了一些足够的条件。
Let $Γ$ be a finite set, and $X\ni x$ a fixed klt germ. For any lc germ $(X\ni x,B:=\sum_{i} b_iB_i)$ such that $b_i\in Γ$, Nakamura's conjecture, which is equivalent to the ACC conjecture for minimal log discrepancies for fixed germs, predicts that there always exists a prime divisor $E$ over $X\ni x$, such that $a(E,X,B)={\rm{mld}}(X\ni x,B)$, and $a(E,X,0)$ is bounded from above. We extend Nakamura's conjecture to the setting that $X\ni x$ is not necessarily fixed and $Γ$ satisfies the DCC, and show it holds for surfaces. We also find some sufficient conditions for the boundedness of $a(E,X,0)$ for any such $E$.
