Toric rings attached to simplicial complexes

Official URL: https://dx.doi.org/10.1007/s13348-025-00493-9

We consider standard graded toric rings whose generators correspond to the faces of a simplicial complex. When is normal, it is shown that its divisor class group is free. For a flag complex which is the clique complex of a perfect graph, a nice description for the class group and the canonical module of in terms of the minimal vertex covers of the graph is given. Moreover, for a quasi-forest simplicial complex a quadratic Gröbner basis for the defining ideal of is presented. Using this fact we give combinatorial descriptions for the a-invariant and the Gorenstein property of.