Abstract
The Chern numbers of the title are the first coefficients (after the multiplicities) of the Hilbert functions of various filtrations of ideals of a local ring (R,m). For a Noetherian (good) filtration A of m-primary ideals, the positivity and bounds for e1(A) are well-studied if R is Cohen-Macaulay, or more broadly, if R is a Buchsbaum ring or mild generalizations thereof. For arbitrary geometric local domains, we introduce techniques based on the theory of maximal CohenMacaulay modules and of extended multiplicity functions to establish the meaning of the positivity of e1(A), and to derive lower and upper bounds for e1(A). Dedicated to Professor Melvin Hochster on the occasion of his 65th birthday
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