偶的F-签名：连续性、p-分形和最小对数偏差
F-signature of pairs: Continuity, p-fractals and minimal log discrepancies
摘要：
本文包含了一些意见的{ $F$ -签名}的三元组$(R,Δ,\ba^t)$在我们以前的联合工作。首先证明了$F$ -签名$s(R,Δ,\ba^t)$作为$t$的函数是连续的，并且对于主理想$\ba$甚至是凸的.然后，我们进一步推导出，对于固定的$t$，$F$ -签名是下半连续的$\Spec R$上的一个功能时，$R$是定期和$\ba$是主要的。我们还指出了密切的关系，在这种设置的签名功能的作品Monsky和Teixeira的希尔伯特-昆兹多重性和$p$ -分形。最后，我们得出结论，表明一个任意的三重$(R,Δ,\ba^t)$的最小日志差异是一个上限的$F$签名。
英文摘要：
This paper contains a number of observations on the {$F$-signature} of triples $(R,Δ,\ba^t)$ introduced in our previous joint work. We first show that the $F$-signature $s(R,Δ,\ba^t)$ is continuous as a function of $t$, and for principal ideals $\ba$ even convex. We then further deduce, for fixed $t$, that the $F$-signature is lower semi-continuous as a function on $\Spec R$ when $R$ is regular and $\ba$ is principal. We also point out the close relationship of the signature function in this setting to the works of Monsky and Teixeira on Hilbert-Kunz multiplicity and $p$-fractals. Finally, we conclude by showing that the minimal log discrepancy of an arbitrary triple $(R,Δ,\ba^t)$ is an upper bound for the $F$-signature.
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