First Coefficient Ideals and the S2-ification of a Rees Algebra

✍ Scribed by Cătălin Ciupercă

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 112 KB
• Volume: 242
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.8835

✦ Synopsis

Let A, ᒊ, k be a d-dimensional d G 1 quasi-unmixed analytically unramified local domain with infinite residue field. If I is an ᒊ-primary ideal, Shah defined the first coefficient ideal of I to be the largest ideal I containing I such that Ä14 ˜n Ž . Ž . Ž . e I s e I for i s 0, 1. Assume that A is S and let S s [ I t be the i i Ä14 2 n n g ‫ޚ‬ w y1 x S -ification of the extended Rees algebra S s A It, t . We prove that I s 2 n Ž n . I for every n G 1. One of the consequences is a procedure of computing first Ä14 coefficient ideals.