Mikhail Ovcharenko offers an alternative definition of weighted generalised Grassmannians to that of Corti-Reid and Qureshi-Szendroi. I will go over the older definition and its difference with the alternative one, giving examples of weighted projective spaces under this point of view. Shortly speaking, the difference lies in considering coweights of (i.e., morphisms from C* to-) GL(W), instead of only SL(W). Ovcharenko exposes properties of Z-gradings and geometric properties of generalised Grassmannians, for which I will try to give an insight.
