On the Seshadri constants of equivariant bundles over Bott-Samelson varieties and wonderful compactifications

Abstract

We study torus-equivariant vector bundles E on a complex projective variety X which is either a Bott-Samelson-Demazure-Hansen variety or a wonderful compactification of a complex symmetric variety of minimal rank. We show that E is nef (respectively, ample) if and only if its restriction to every torus-invariant curve in X is nef (respectively, ample). We also compute the Seshadri constants ε(E, x), where x ∈ X is any point fixed by the action of a maximal torus.