On some cconjectures about the Chern numbers of filtrations

2010/01/16 by Mousumi Mandal, Balwant Singh, Mandal, Mousumi +3 · 1 citation
Mathematics · #13H15 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13H15

paper · pdf · doi:10.48550/arxiv.1001.2822

20 pages

arxiv created 2010/01/16 · arxiv updated 2010/02/26

Abstract

Let I be an m-primary ideal of a Noetherian local ring (R,m) of positive dimension. The coefficient e₁(A) of the Hilbert polynomial of an I-admissible filtration A is called the Chern number of A. The Positivity Conjecture of Vasconcelos for the Chern number of the integral closure filtration Iⁿ 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.

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