On some conjectures about the Chern numbers of filtrations

详细信息    查看全文

• 作者：Mousumi M ; al ; Balwant Singh ; J.K. Verma
• 关键词：Chern number ; Hilbert polynomial ; Cohen– ; Macaulay ring ; Face ring ; Filtration of ideals
• 刊名：Journal of Algebra
• 出版年：2011
• 出版时间：1 January 2011
• 年：2011
• 卷：325
• 期：1
• 页码：147-162
• 全文大小：232 K

文摘

Let I be an -primary ideal of a Noetherian local ring of positive dimension. The coefficient of the Hilbert polynomial of an I-admissible filtration is called the Chern number of . The Positivity Conjecture of Vasconcelos for the Chern number of the integral closure filtration is proved for a 2-dimensional complete local domain and more generally for any analytically unramified local ring R whose integral closure in its total ring of fractions is Cohen–Macaulay as an R-module. It is proved that if I is a parameter ideal then the Chern number of the I-adic filtration is non-negative. Several other results on the Chern number of the integral closure filtration are established, especially in the case when R is not necessarily Cohen–Macaulay.