论文标题
低阶的差分运算符的分辨率，用于孤立的超表面奇异性
Resolutions of differential operators of low order for an isolated hypersurface singularity
论文作者
论文摘要
在本文中，我们开发了一种新的方法，用于研究一个孤立的奇异性分级超表面环$ r $的差分操作员，该操作员在特征零的领域中定义了仿射三个空间的表面。通过这种方法，我们为第二和第三的差分运算符的模块构建了一个显式的最小生成集，以及其最小的免费分辨率；这扩大了Bernstein，Gel'Fand和Gel'Fand和Vigué的结果。我们的构建部分依赖于我们在$ r $的奇异性类别中得出的这些模块的描述。也就是说，我们构建了从残基字段开始的明确矩阵因素化。
In this paper we develop a new approach for studying differential operators of an isolated singularity graded hypersurface ring $R$ defining a surface in affine three-space over a field of characteristic zero. With this method, we construct an explicit minimal generating set for the modules of differential operators of order two and three, as well as their minimal free resolutions; this expands results of Bernstein, Gel'fand, and Gel'fand and of Vigué. Our construction relies, in part, on a description of these modules that we derive in the singularity category of $R$. Namely, we build explicit matrix factorizations starting from that of the residue field.
