Linkage by Generically Gorenstein, Cohen–Macaulay Ideals

✍ Scribed by Heath M. Martin

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 312 KB
• Volume: 207
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7461

✦ Synopsis

In this paper, we study linkage by a wider class of ideals than the complete intersections. We are most interested in how the Cohen᎐Macaulay property behaves along this more general notion of linkage. In particular, if ideals A and B are linked by a generically Gorenstein Cohen᎐Macaulay ideal I, and if A is a Cohen᎐Macaulay ideal, we give a criterion for B to be a Cohen᎐Macaulay ideal. When RrB is not Cohen᎐Macaulay, we can give in many cases an easy description of the non᎐Cohen᎐Macaulay locus of RrB, and also a criterion for RrB to have almost maximal depth.