论文标题
通过saito的对数残留物来计算常规的杂晶差分形式
Computing Regular Meromorphic Differential Forms via Saito's Logarithmic Residues
论文作者
论文摘要
在计算复杂分析的背景下，考虑了与孤立奇异性相关的对数差分形式和对数与超表面相关的对数矢量场。作为应用，研究了D. Barlet和M. Kersken引入的A.G. A.G. A.G. A.G. A.G. A.G. A.G. A.G.的常规Meromorormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormorormormormormormormormormormormormormormormormormormormormormormormormormorphial形式，并研究了Brieskorn Formulas在高斯曼宁（Gauss-Manin Connections）上的Brieskorn公式。 （i）一种方法是通过saito的对数残基来描述常规杂形差分形式的奇异部分。通过使用示例来说明所得算法。 （ii）发现了Brieskorn公式与对数矢量场之间的新链接，并以非平凡的对数矢量字段来重写Brieskorn公式的表达式。描述了一种新的有效方法来计算适合计算高斯 - 曼宁连接的非琐碎对数矢量场。举例说明了一些示例。
Logarithmic differential forms and logarithmic vector fields associated to a hypersurface with an isolated singularity are considered in the context of computational complex analysis. As applications, based on the concept of torsion differential forms due to A.G. Aleksandrov, regular meromorphic differential forms introduced by D. Barlet and M. Kersken, and Brieskorn formulae on Gauss-Manin connections are investigated. (i) A method is given to describe singular parts of regular meromorphic differential forms in terms of non-trivial logarithmic vector fields via Saito's logarithmic residues. The resulting algorithm is illustrated by using examples. (ii) A new link between Brieskorn formulae and logarithmic vector fields is discovered and an expression that rewrites Brieskorn formulae in terms of non-trivial logarithmic vector fields is presented. A new effective method is described to compute non trivial logarithmic vector fields which are suitable for the computation of Gauss-Manin connections. Some examples are given for illustration.
