Universal parameters for Stanley-Reisner rings and a colorful Hochster formula
- Victor Reiner (University of Minnesota - Twin Cities, Minneapolis, USA)
The Stanley-Reisner ring R of any simplicial complex contains a "universal" family of elements that form an h.s.o.p. (homogeneous system of parameters): the elementary symmetric functions in the vertex variables. This talk will discuss an interesting depth-detection property of this universal h.s.o.p., as well as a conjecture on the shape of the minimal free resolution of the ring R over this universal parameter ring. This conjecture is closely connected to a generalization of Hochster's formula on resolutions of Stanley-Reisner rings, one that applies to any proper vertex-coloring of the simplicial complex.