论文标题
双线性在雅各布模块中形式和$ n $ spectral链的束缚链，隔离奇异性
Bilinear forms in the Jacobian module and binding of $N$-spectral chains of a hypersurface with an isolated singularity
论文作者
论文摘要
Lefschetz利用他用超平面剪切的深层概念来解释了如何通过他称为原始同源性的基本作品来构建射影平滑品种的同源组。每当我们拥有带有双层形式的矢量空间（即带有杯子产品的同源性）和$ \ pm $ - $ smmperric的nilpotent操作员（即用超平面切割）时，就可以应用这个想法。我们将在奇异理论的背景下说明这一点：由$ f = 0 $定义的超脸的孤立奇异点的细菌。我们从奇异性的Jacobian（或Milnor）代数的代数设置开始，将Grothendieck配对为双线性形式，并将乘以$ F $作为对称的Nilpotent运算符。我们继续以杯子产物引起的双线性形式消失的拓扑设置，并作为nilpotent映射单一单位图作为反对称操作员的一能映射的对数。然后，我们展示了这两个截然不同的设置如何使用Brieskorn晶格作为D模块，在使用Brieskorn（1970），A。Varchenko（1980年代），M。Saito（1989）和C. Hertling（1999，2004，2005）上，引起了极地的Bighod hodge结构（singlible and the Enlum and seneen of the Entrybrighte and seneen of the seneen offerement and seneen offerement and seneen offerement and seneen，比代数单构型的特征值更深入。特别是，我们展示了如何通过将它们粘在Brieskorn Lattice中，从几个$ n $ -jordan的链中获得了$ f $ -Jordan的链条。
Using his deep and beautiful idea of cutting with a Hyperplane, Lefschetz explained how the homology groups of a projective smooth variety could be constructed from basic pieces, that he called primitive homology. This idea can be applied every time we have a vector space with a biliner form (i.e. homology with cup product) and a $\pm$-symmetric nilpotent operator (i.e. cutting with a hyperplane). We will illustrate this in the context of Singularity Theory: A germ of an isolated singular point of a hypersurface defined by $f=0$. We begin with the algebraic setting in the Jacobian (or Milnor) Algebra of the singularity, with Grothendieck pairing as bilinear form and multiplication by $f$ as a symmetric nilpotent operator. We continue in the topological setting of vanishing cohomology with bilinear form induced from cup product and as nilpotent map the logarithm of the unipotent map of the monodromy as an anti-symmetric operator. We then show how these 2 very different settings are tied up using the Brieskorn lattice as a D-module, on using results of Brieskorn (1970), A. Varchenko (1980s), M. Saito (1989), and C. Hertling (1999, 2004, 2005), inducing a Polarized Mixed Hodge structure at the singularity (Steenbrink, 1976) and bringing the spectrum of the singularity as a deeper invariant than the eigenvalues of the Algebraic Monodromy. In particular, we show how an $f$-Jordan chain is obtained from several $N$-Jordan chains by gluing them in the Brieskorn lattice.
