论文标题
通过Bernstein-Sato多项式的根源进行F-跳跃数字的估计值
An estimate for F-jumping numbers via the roots of the Bernstein-Sato polynomial
论文作者
论文摘要
给定$ x $上的平滑复杂的代数$ x $和非零的常规功能$ f $，我们对跳跃数量$ f $的跳跃数量与$ f $ f $ dyauction $ f_p $ f $ f $ f $ f $ f $ f $ f $ p \ gg 0 $之间的差异有效估计。作为一个应用程序，我们表明，如果$ b_f $没有形式的$ - {\ rm lct}（f） - n $，则具有$ n $ a a正整数，那么$ f $ f $ f_p $的阈值等于$ p \ g g gg gg gg 0 $（p \ g g c \ c）（p-1）（p-1）（p-1） {\ Mathbf Z} $。
Given a smooth complex algebraic variety $X$ and a nonzero regular function $f$ on $X$, we give an effective estimate for the difference between the jumping numbers of $f$ and the $F$-jumping numbers of a reduction $f_p$ of $f$ to characteristic $p\gg 0$, in terms of the roots of the Bernstein-Sato polynomial $b_f$ of $f$. As an application, we show that if $b_f$ has no roots of the form $-{\rm lct}(f)-n$, with $n$ a positive integer, then the $F$-pure threshold of $f_p$ is equal to the log canonical threshold of $f$ for $p\gg 0$ with $(p-1){\rm lct}(f)\in {\mathbf Z}$.
