Hyukmoon Choi, Equivariant compactification structures on smooth projective horospherical varieties of Picard number 1

A projective variety V is an equivariant compactification of an algebraic group G if there exists an algebraic G-action on V with a Zariski open orbit O, which is equivariantly biregular to G. Such a G-action is called an equivariant compactification (EC) structure on V. For a smooth nonhomogeneous projective horospherical variety X of Picard number 1, and for a suitable nilpotent subgroup N of the automorphism group of X, we show that X admits an EC structure of N and that any two EC structures of N on X are isomorphic.