Singular del Pezzo surfaces that are equivariant compactifications

We determine which singular del Pezzo surfaces are equivariant compactifications of $\mathbb G_\mathrm a^2$, to assist with proofs of Manin's conjecture for such surfaces. Additionally, we give an example of a singular quartic del Pezzo surface that is an equivariant compactification of $\mathbb G_\mathrm a\rtimes\mathbb G_\mathrm m$. Bibl. 32 titles.