Equivariant vector bundles on complete symmetric varieties of minimal rank

Abstract

Let X be the wonderful compactification of a complex symmetric space G/H of minimal rank. For a point x ∈ G, denote by Z the closure of BxH/H in X, where B is a Borel subgroup of G. The universal cover of G is denoted by [Formula: see text]. Given a [Formula: see text] equivariant vector bundle E on X, we prove that E is nef (respectively, ample) if and only if its restriction to Z is nef (respectively, ample). Similarly, E is trivial if and only if its restriction to Z is so.

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

“…An affirmative answer is also given when E is any line bundle on a flag variety over a projective curve defined over the algebraic closure of a finite field [4]. A related question was studied in [3] for equivariant vector bundles on wonderful compactifications.…”