Abstract:
In this talk, I will present the result of recent joint work with Martina Kubitzke. We begin with a review of Grassmann-Plücker ideals and how they are related to the Hibi rings of certain posets as well as unimodular triangulations of their order polytopes. We then construct an initial ideal for the Grassmann-Plücker ideal of planes in n-dimensional space that is the Stanley-Reisner ideal of the join of a simplex and the simplicial associahedron. For that, we use a special case of reverse lexicographic triangulations as introduced by Athanasiadis. Finally, we discuss the case of Grassmann-Plücker ideals of higher-dimensional subspaces where analogous results are still to be found.