寻找不变量来对几何对象进行分类一直是几何学的重要课题。J. Mather 和Stephen Yau 在 1982 年成功地使用模代数完全刻画了超曲面奇点。本文中，我们将针对超曲面奇点给出一系列新的不变量，这些不变量被称作是高阶奇点迹模代数，可以视作是模代数的高阶类比物。设 ? 为满足某些条件的分次代数。? 的导子全体，记为 Der(?)，也为分次代数。一个自然的问题是这个代数是否有负权重导子？很多数学家从不同领域出发提出了类似的猜想。Halperin 猜测一个分次完全交阿廷代数没有负权重导子。这个猜想在有理同伦论中非常重要。如果这个猜想成立，可以说明一大类满足某些条件的塞尔纤维化的塞尔谱序列在 ?2 收敛。Stephen Yau 考虑模代数的导子李代数（被称作是 Yau 代数）并用其给了拟齐次奇点的一个微局部特征。Stephen Yau 猜测孤立加权齐次超曲面奇点的模代数没有负权重导子。Wahl 和 Aleksandrov 也从其他角度提出过类似的猜想。这些猜想至今仍未被解决。只有一些部分结果是已经得到的。本文中，我们针对孤立加权齐次超曲面奇点的高阶奇点迹模代数提出了类似的负权重导子不存在性的猜想。并且针对低维和带有某些权重关系的情形给出了证明。我们同样利用某些高阶奇点迹模代数（及其导子代数）给出了拟齐次奇点的微局部特征。

Finding invariants to classify geometric objects has always been an important topic in geometry. J. Mather and Stephen Yau successfully use moduli algebra to classify hypersurface singularities in 1982. In this thesis, we also arise a series of hypersurface singularities invariants, called higher singular locus moduli algebra.Let ? be graded algebra with some conditions. We denote all the derivations of ? by Der(?), which is also graded. A natural question is does this algebra have negative weight derivatives? Many mathematicians from different fields have come up with similar conjectures. Halperin conjecture that a graded complete intersection Artin algebra does not have negative weight derivations. This conjecture is very important in rational homotopy theory. If this conjecture holds, then the Serre spectral sequence for a certainSerre fibration collapses at ?2. Stephen Yau considers the Lie algebra of derivations of the moduli algebra (called Yau algebra) and gives a micro-local characterization of quasi-homogeneous. Stephen Yau conjectured that the moduli algebra of an isolated weighted homogeneous hypersurface singularity does not have negative weight derivations. Wahl and Aleksandrov also arise similar conjectures from other settings. All those conjectures are open now. Only some partial results hold.In this thesis, we arise some new conjecture that higher singular locus moduli algebra of an isolated weighted homogeneous hypersurface singularity does not have negative weight derivations. We proved that in low-dimension cases or adding some weight conditions this conjecture is true. We also use some higher singular locus algebras (and their derivation algebras) to get a micro-local characterization of quasi-homogeneous.