Zariski的维度奇点类型。维度类型为2的情况

IF 0.9 1区 数学 Q2 MATHEMATICS
A. Parusiński, L. Paunescu
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引用次数: 3

摘要

20世纪70年代,O.Zariski提出了特征为零的代数封闭域上的代数体和代数超曲面的等奇异性的一般理论。他的理论建立在理解超曲面奇点的维数类型的基础上,这一概念是通过考虑连续的“一般”corank 11投影的判别位点而递归定义的。维度类型1的奇点理论,即一般出现在余维度1中的奇点理论是由Zariski在其关于平面曲线奇点的等奇异族的基础论文中提出的。在本文中,我们通过研究三维空间中不一定孤立的表面奇点的Zariski等奇异族,完全解决了维度类型2的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Zariski’s dimensionality type of singularities. Case of dimensionality type 2
In the 1970s O. Zariski introduced a general theory of equisingularity for algebroid and algebraic hypersurfaces over an algebraically closed field of characteristic zero. His theory builds up on understanding the dimensionality type of hypersurface singularities, notion defined recursively by considering the discriminants loci of successive “generic” corank 1 1 projections. The theory of singularities of dimensionality type 1, that is the ones appearing generically in codimension 1, was developed by Zariski in his foundational papers on equisingular families of plane curve singularities. In this paper we completely settle the case of dimensionality type 2, by studying Zariski equisingular families of surfaces singularities, not necessarily isolated, in the three-dimensional space.
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来源期刊
CiteScore
2.70
自引率
5.60%
发文量
23
审稿时长
>12 weeks
期刊介绍: The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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