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

TL;DR

This paper determines the automorphism groups of generalized Kausz compactifications and spaces of complete collineations by analyzing their geometric properties and anticanonical bundles.

Contribution

It provides the first comprehensive determination of automorphism groups for these generalized compactifications and collineation spaces, extending previous work on Grassmannian blow-ups.

Findings

Automorphism groups of $ ext{Kausz}$ compactifications are explicitly characterized.

Positivity of anticanonical bundles is established for these spaces.

Results extend prior work on Grassmannian blow-ups.

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).