The Chern Coefficients of Local Rings
نویسنده
چکیده
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 Cohen-Macaulay 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).
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