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    On the Chern number of II-admissible filtrations of ideals

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    Let II be an \m-primary ideal of a Noetherian local ring (R, \m) of positive dimension. The coefficient e1(I)e_1(\mathcal I) of the Hilbert polynomial of an II-admissible filtration I\mathcal I is called the Chern number of I\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(I)e_1(\mathcal I)