Serre’s Condition R k for Sums of Geometric Links

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• 作者：Mark Johnson ; Bernd Ulrich
• 关键词：Residual intersection ; Linkage ; Serre’s condition R k ; Artin ; Nagata property ; Finite projective dimension ; Complete intersection ; Primary 13C40 ; 14M06 ; Secondary 13D02 ; 13E15
• 刊名：Acta Mathematica Vietnamica
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：40
• 期：3
• 页码：393-401
• 全文大小：214 KB
• 参考文献：1.Bertini, E.: Introduzione alla geometria proiettiva degli iperspazi. Enrico Spoerri, Pisa (1907)
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• 作者单位：Mark Johnson (1)
  Bernd Ulrich (2)
  
  1. Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, USA
  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144

文摘

We investigate what it means that the intersection of a variety with a residual intersection has a low-dimensional singular locus. For schemes having Cohen-Macaulay residual intersections, we prove, for instance, that if the intersection of the scheme with one of its geometric residual intersections has a ‘small-singular locus, then the scheme can be defined by ‘few-equations locally. Keywords Residual intersection Linkage Serre’s condition R _k Artin-Nagata property Finite projective dimension Complete intersection