Explicit description of weighted Grassmannians

A weighted Grassmannian is a closed subvariety of a weighted projective space defined by (weighted-homogeneous) Plücker relations. They were introduced by Corti–Reid–Grojnowski in order to construct complete intersections therein with given geometric properties. Unfortunately, their explicit construction of weighted Grassmannians does not yield all possible Z-gradings on Plücker coordinates. In the talk we will discuss how one can remedy this, and why this allows us to construct new examples of Q-Fano varieties with canonical or terminal singularities.