论文标题
lyubeznik数字，$ f $ - 模块和广义分数的模块
Lyubeznik numbers, $F$-modules and modules of generalized fractions
论文作者
论文摘要
本文提出了一种用于计算本地环数字的算法，该算法是普通本地环$ r $的同态图像。所使用的方法采用了$ r $ $ r $的$ f $ modules，尤其是他的$ f $ finite $ f $ - 模块，以及夏普和Zakeri的广义分数的模块。结果表明，$ r $的许多广义分数模块都具有天然结构，例如$ f $ - 模块；这些导致$ f $模块结构在$ r $的某些本地共同体模块上，并与$ f $ - 模块结构相结合，这些结构是由huneke and Sharp的工作造成的，$ r $ r $ r $ - 模块，以计算lyubeznik数字。所得算法已在Macaulay2中实现。
This paper presents an algorithm for calculation of the Lyubeznik numbers of a local ring which is a homomorphic image of a regular local ring $R$ of prime characteristic. The methods used employ Lyubeznik's $F$-modules over $R$, particularly his $F$-finite $F$-modules, and also the modules of generalized fractions of Sharp and Zakeri. It is shown that many modules of generalized fractions over $R$ have natural structures as $F$-modules; these lead to $F$-module structures on certain local cohomology modules over $R$, which are exploited, in conjunction with $F$-module structures on injective $R$-modules that result from work of Huneke and Sharp, to compute Lyubeznik numbers. The resulting algorithm has been implemented in Macaulay2.
