  We classify generically transitive actions of semidirect products of an
additive and a multiplicative group on the projective plane. Motivated by the
program to study the distribution of rational points on del Pezzo surfaces
(Manin's conjecture), we determine all (possibly singular) del Pezzo surfaces
that are equivariant compactifications of homogeneous spaces for such
semidirect products.

Algebraic Geometry;Number Theory