عنوان	Toric rings attached to simplicial complexes
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	toric rings, quasi-forests, normal rings, canonical module
چکیده	We consider standard graded toric rings $R_{\Delta}$ whose generators correspond to the faces of a simplicial complex $\Delta$. When $R_{\Delta}$ is normal, it is shown that its divisor class group is free. For a flag complex $\Delta$ which is the clique complex of a perfect graph, a nice description for the class group and the canonical module of $R_{\Delta}$ in terms of the minimal vertex covers of the graph is given. Moreover, for a quasi-forest simplicial complex a quadratic Gr\"obner basis for the defining ideal of $R_{\Delta}$ is presented. Using this fact we give combinatorial descriptions for the $a$-invariant and the Gorenstein property of $R_\Delta$.
پژوهشگران	یورگن هرزوگ (نفر اول)، سمیه مرادی (نفر دوم)، آیشه اسلوب قریشی (نفر سوم)