On the Chern number of I-admissible filtrations of ideals

2012/05/02 by Mousumi Mandal, Mandal, Mousumi, J. K. Verma +1
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.1205.0390

arxiv created 2012/05/02 · arxiv updated 2012/05/03

Abstract

Let I be an \m-primary ideal of a Noetherian local ring (R, \m) of positive dimension. The coefficient e₁(\mathcal I) of the Hilbert polynomial of an I-admissible filtration \mathcal I is called the Chern number of \mathcal I. A formula for the Chern number has been derived involving Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e₁(\mathcal I).

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