Results | SCSU Bibliography

Ghezzi, L., & Hong, J. (2025). Degrees: Vasconcelos contributions. De Gruyter Proc. Math., 203–240. https://doi.org/10.1515/9783110999365-006

A degree of a module M is a numerical measure of information carried by M. We highlight some of Vasconcelos’ outstanding contributions to the theory of degrees, bridging commutative algebra and computational algebra. We present several degrees he introduced and developed, including arithmetic degree, jdeg, homological degree, cohomological degrees, canonical degree, and bicanonical degree. For the canonical and bicanonical degrees, we discuss recent developments motivated by our joint works [25, 19, 9]. ©2025 Walter de Gruyter GmbH,Berlin/Boston.

Ghezzi, L., Hong, J., & Vasconcelos, W. V. (2009). The signature of the chern coefficients of local rings. Mathematical Research Letters, 16(2), 279–289. https://doi.org/201308301946

This paper considers the following conjecture: If R is an unmixed, equidimensionallocal 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 catenary integral domains containing fields. Criteria for the detection of Cohen-Macaulayness in equi-generated graded modules are derived. © International Press 2009.

View on adsabs.harvard.edu

Ghezzi, L., Goto, S., Hong, J., & Vasconcelos, W. V. (2017). Invariants of Cohen–Macaulay rings associated to their canonical ideals. Journal of Algebra, 489, 506–528. https://doi.org/10.1016/j.jalgebra.2017.05.042

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.

View on core.ac.uk

Ghezzi, L., Goto, S., Hong, J., & Vasconcelos, W. V. (2013). Variation of hilbert coefficients. Proceedings of the American Mathematical Society, 141(9), 3037–3048. https://doi.org/10.1090/S0002-9939-2013-11774-0

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.

View on www.ams.org

Ghezzi, L., Goto, S., Hong, J., Hutson, H. L., & Vasconcelos, W. V. (2021). The bi-canonical degree of a Cohen–Macaulay ring. Journal of Algebra, 571, 55–74. https://doi.org/10.1016/j.jalgebra.2018.12.013

This paper is a sequel to [8] where we introduced an invariant, called canonical degree, of Cohen–Macaulay local rings that admit a canonical ideal. Here to each such ring R with a canonical ideal, we attach a different invariant, called bi-canonical degree, which in dimension 1 appears also in [12] as the residue of R. The minimal values of these functions characterize specific classes of Cohen–Macaulay rings. We give a uniform presentation of such degrees and discuss some computational opportunities offered by the bi-canonical degree. © 2019 Elsevier Inc.

View on lens.org

Ghezzi, L., Goto, S., Hong, J., Ozeki, K., Phuong, T. T., & Vasconcelos, W. V. (2012). Variation of the first hilbert coefficients of parameters with a common integral closure. Journal of Pure and Applied Algebra, 216(1), 216–232. https://doi.org/10.1016/j.jpaa.2011.06.008

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.

View on adsabs.harvard.edu

Ghezzi, L., Goto, S., Hong, J., Ozeki, K., Phuong, T. T., & Vasconcelos, W. V. (2010). Cohen–Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals. Journal of The London Mathematical Society-Second Series, 81(3), 679–695. https://doi.org/10.1112/jlms/jdq008

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.

View on 128.84.21.199

Ghezzi, L., Goto, S., Hong, J., Ozeki, K., Phuong, T. T., & Vasconcelos, W. V. (2015). The chern numbers and euler characteristics of modules. Acta Mathematica Vietnamica, 40(1), 37–60. https://doi.org/10.1007/s40306-014-0096-6

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.

View on core.ac.uk

Endo, N., Ghezzi, L., Goto, S., Hong, J., Iai, S.-I., Kobayashi, T., Matsuoka, N., & Takahashi, R. (2025). Rings with q-torsionfree canonical modules. De Gruyter Proc. Math., 405–426. https://doi.org/10.1515/9783110999365-014

Let A be a Noetherian local ring with canonical module KA. We characterize A when KA is a torsionless, reflexive, or q-torsionfree module for an integer q ≥ 3. If A is a Cohen–Macaulay ring, H.-B. Foxby proved in 1974 that the A-module KA is q-torsionfree if and only if the ring A is q-Gorenstein. With mild assumptions, we provide a generalization of Foxby’s result to arbitrary Noetherian local rings admitting the canonical module. In particular, since the reflexivity of the canonical module is closely related to the ring being Gorenstein in low codimension, we also explore quasinormal rings, introduced by W. V. Vasconcelos. We provide several examples as well. ©2025 Walter de Gruyter GmbH,Berlin/Boston.

Your search

Results 9 resources

Explore

Resource type

Publication year

Resource language