The homology of parameter ideals - Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer V (Journal of Algebra, 2012)
For a Noetherian local ring, we analyze conjectural relationships between the first Hilbert coefficient of a parameter ideal and the first partial Euler characteristic of its Koszul complex. Given their similar role as predictors of the Cohen-Macaulay property, we consider a direct comparison between them. For parameter ideals generated by d-sequences these numbers are related in an explicit formula. We then turn to study of families of parameter ideals that have the same Hilbert function. © 2012 Elsevier Inc.
7 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/105-439-048-396-373 tex.type: [object Object]
Keywords: Cohen-Macaulay ring; D-sequence; Euler characteristic; Hilbert coefficient; Hilbert function; dept.mat; peer-reviewed