Invariants of Cohen–Macaulay rings associated to their canonical ideals - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer V (Journal of Algebra, 2017)
The purpose of this paper is to introduce new invariants of Cohen–Macaulay local rings. Our focus is the class of Cohen–Macaulay local rings that admit a canonical ideal. Attached to each such ring R with a canonical ideal C, there are integers–the type of R, the reduction number of C–that provide valuable metrics to express the deviation of R from being a Gorenstein ring. We enlarge this list with other integers–the roots of R and several canonical degrees. The latter are multiplicity based functions of the Rees algebra of C. © 2017 Elsevier Inc.
8 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/157-904-936-372-561 tex.type: [object Object]
Keywords: Analytic spread; Canonical degree; Cohen–Macaulay type; Reduction number; Roots; dept.mat; peer-reviewed

Variation of hilbert coefficients - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer V (Proceedings of the American Mathematical Society, 2013)
For a Noetherian local ring (R, m), the first two Hilbert coefficients, e0 and e1, of the I-adic filtration of an m-primary ideal I are known to code for properties of R, of the blowup of Spec(R) along V (I), and even of their normalizations. We give estimations for these coefficients when I is enlarged (in the case of e1 in the same integral closure class) for general Noetherian local rings. © American Mathematical Society.
3 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/035-873-690-231-781
Keywords: dept.mat

Variation of the first hilbert coefficients of parameters with a common integral closure - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Ozeki, Kazuho; Phuong, Tran Thi; Vasconcelos, Wolmer V (Journal of Pure and Applied Algebra, 2012)
A problem posed by Vasconcelos [33] on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well. © 2011 Elsevier B.V.
2 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/054-357-014-729-224 tex.type: [object Object]
Keywords: Primary; Secondary; dept.mat

Cohen–Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Ozeki, Kazuho; Phuong, Tran Thi; Vasconcelos, Wolmer V (Journal of The London Mathematical Society-second Series, 2010)
The conjecture of Wolmer Vasconcelos on the vanishing of the first Hilbert coefficient e1(Q) is solved affirmatively, where Q is a parameter ideal in a Noetherian local ring. Basic properties of the rings for which e 1(Q) vanishes are derived. The invariance of e1(Q) for parameter ideals Q and its relationship to Buchsbaum rings are studied. © 2010 London Mathematical Society.
26 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/176-080-348-377-227 tex.type: [object Object]
Keywords: dept.mat

The chern numbers and euler characteristics of modules - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Ozeki, Kazuho; Phuong, Tran Thi; Vasconcelos, Wolmer V (Acta Mathematica Vietnamica, 2015)
The set of the first Hilbert coefficients of parameter ideals relative to a module—its Chern coefficients—over a local Noetherian ring codes for considerable information about its structure–noteworthy properties such as that of Cohen-Macaulayness, Buchsbaumness, and of having finitely generated local cohomology. The authors have previously studied the ring case. By developing a robust setting to treat these coefficients for unmixed rings and modules, the case of modules is analyzed in a more transparent manner. Another series of integers arise from partial Euler characteristics and are shown to carry similar properties of the module. The technology of homological degree theory is also introduced in order to derive bounds for these two sets of numbers. © 2014, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
4 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/029-408-859-697-122
Keywords: Buchsbaum module; Cohen-Macaulay module; Euler characteristic; Generalized Cohen-Macaulay module; Hilbert coefficient; Hilbert function; Local cohomology; Parameter ideal; Vasconcelos module; dept.mat