$\mathbb{Z}^r$-graded rings and their canonical modules
Commutative Algebra
2025-05-19 v1
Abstract
In ``Cohen--Macaulay rings'' Bruns and Herzog define the graded canonical module for -graded rings. We generalize the definition to multigradings and prove that the canonical module ``localizes''. As an application, we give a divisorial proof of the theorem of Danilov and Stanley on the canonical module of affine normal monoid rings. Along the way, we develop the basic theory of multigraded rings and modules.
Cite
@article{arxiv.2505.11402,
title = {$\mathbb{Z}^r$-graded rings and their canonical modules},
author = {Margherita Barile and Winfried Bruns},
journal= {arXiv preprint arXiv:2505.11402},
year = {2025}
}