The trace of the canonical module: algebra and combinatorics
Dumitru Stamate (University of Bucharest, Romania)
Abstract: Let R be a Cohen-Macaulay local ring (or positively graded K-algebra) with canonical module $\omega_R.$ The trace of the latter, $tr(\omega_R),$ is by definition, the ideal generated by the images of all R-module homomorphisms from $\omega_R$ into R. Since this ideal describes the non-Gorenstein locus of R, it can be viewed as a way to measure how far is R from being Gorenstein.
In terms of this ideal, new classes of rings have been introduced, and their properties are under scrutiny. We discuss some of these approaches, with a special focus on families of examples coming from combinatorics.
This talk is based on joint works with J. Herzog, T. Hibi, R. Jafari and S. Kumashiro.
Mathematics
Audience: advanced learners
IIT Bombay Virtual Commutative Algebra Seminar
Series comments: Note: To get meeting ID,fill the Google form on the web-site of the series sites.google.com/view/virtual-comm-algebra-seminar/home
Organizers: | Jugal Kishore Verma*, Kriti Goel*, Parangama Sarkar, Shreedevi Masuti |
Curator: | Saipriya Dubey* |
*contact for this listing |