Testing zero-dimensionality of varieties at a point
Testing zero-dimensionality of varieties at a point
复制标题
在一点测试品种的零维性
DOI：
10.1007/s11786-020-00484-y
复制
发表时间：
2021
影响因子：
0.8
通讯作者：
K. Nabeshima and S. Tajima
中科院分区：
文献类型：
--
作者：
深作亮太;田島慎一;K. Nabeshima and S. Tajima
介绍了一种有效的方法来检验品种在一点上的零维性。本文的目的是计算和分析孤立超曲面奇异点的变形。作为应用，还描述了用于计算局部维度的方法。对于一个给定的理想包含参数的情况下，所提出的算法可以输出，特别是一个分解的参数空间到层根据当地的尺寸在一个点的相关品种。所提出的算法的关键是使用全面的Gröbner系统的概念。
Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing local dimensions are also described. For the case where a given ideal contains parameters, the proposed algorithms can output in particular a decomposition of a parameter space into strata according to the local dimension at a point of the associated varieties. The key of the proposed algorithms is the use of the notion of comprehensive Gröbner systems.