The trace of the canonical module: algebra and combinatorics

Dumitru Stamate (University of Bucharest, Romania)

10-Sep-2021, 12:00-13:00 (3 years ago)

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*
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