Generalization of bi-canonical degrees

Authors

Joseph Brennan, University of Central FloridaFollow
Laura Ghezzi, CUNY New York City College of TechnologyFollow
Jooyoun Hong, Southern Connecticut State UniversityFollow
Wolmer Vasconcelos, Rutgers University - New Brunswick/Piscataway

Document Type

Article

Publication Date

9-1-2022

Abstract

We discuss invariants of Cohen-Macaulay local rings that admit a canonical module ω. Attached to each such ring R, when ω is an ideal, there are integers–the type of R, the reduction number of ω–that provide valuable metrics to express the deviation of R from being a Gorenstein ring. In (Ghezzi et al. in JMS 589:506–528, 2017) and (Ghezzi et al. in JMS 571:55–74, 2021) we enlarged this list with the canonical degree and the bi-canonical degree. In this work we extend the bi-canonical degree to rings where ω is not necessarily an ideal. We also discuss generalizations to rings without canonical modules but admitting modules sharing some of their properties.

Comments

Brennan, J., Ghezzi, L., Hong, J. et al. Generalization of bi-canonical degrees. São Paulo J. Math. Sci. (2022). https://doi.org/10.1007/s40863-022-00333-9. Preprint at https://arxiv.org/abs/2209.02798