Transformations of Grassmannians preserving the class of base subsets

Abstract.

Let $\mathcal{P}$ be a finite-dimensional projective space and $\mathcal{G}_k$ be the Grassmannian consisting of all k-dimensional subspaces of $\mathcal{P}$. In the paper we show that transformations of $\mathcal{G}_k$ sending base subsets to base subsets are induced by collineations of $\mathcal{P}$ to itself or to the dual projective space $\mathcal{P}^*$. This statement generalizes the main result of the author’s paper [19].