论文标题
圆锥体上的F-签名函数
The F-signature Function on the Ample Cone
论文作者
论文摘要
对于在阳性特征的代数闭合场上的任何固定的全球formular投射品种X，我们研究X截面环相对于X上的丰富Cartier除数的F-签名。特别是，我们在X的充足锥上定义了F-签名功能，并显示了它局部的LipsChitz持续。我们进一步证明了F-签名函数延伸到富锥的边界。我们还建立了F-签名函数与丰富锥体上体积函数之间的有效比较。结果，我们表明，对于nef但不大的除数，F-签名的扩展为零。
For any fixed globally F-regular projective variety X over an algebraically closed field of positive characteristic, we study the F-signature of section rings of X with respect to the ample Cartier divisors on X. In particular, we define an F-signature function on the ample cone of X and show that it is locally Lipschitz continuous. We further prove that the F-signature function extends to the boundary of the ample cone. We also establish an effective comparison between the F-signature function and the volume function on the ample cone. As a consequence, we show that for divisors that are nef but not big, the extension of the F-signature is zero.
