The automorphism groups of generalized Kausz compactifications and spaces of complete collineations

Abstract

In this paper, we determine the automorphism groups of generalized Kausz compactifications ${\mathcal{T}}_{s,p,n}$. By establishing the (semi-)positivity of the anticanonical bundles of ${\mathcal{T}}_{s,p,n}$, we also determine the automorphism groups of generalized spaces of complete collineations ${\mathcal{M}}_{s,p,n}$. The results in this paper are partially taken from the author's earlier arxiv post (Canonical blow-ups of grassmann manifolds, arxiv:2007.06200).