A note on Chern coefficients and Cohen–Macaulay rings
نویسندگان
چکیده
منابع مشابه
The Chern Coefficients of Local Rings
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 geomet...
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This paper considers the following conjecture: If R is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal J generated by a system of parameters, the Chern coefficient e1(J) < 0 is equivalent to R being non Cohen-Macaulay. The conjecture is established if R is a homomorphic image of a Gorenstein ring, and for all universally cate...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 2020
ISSN: 0004-2080,1871-2487
DOI: 10.4310/arkiv.2020.v58.n1.a12