  We prove new local inequality for divisors on surfaces and utilize it to
compute $\alpha$-invariants of singular del Pezzo surfaces, which implies that
del Pezzo surfaces of degree one whose singular points are of type
$\mathbb{A}_{1}$, $\mathbb{A}_{2}$, $\mathbb{A}_{3}$, $\mathbb{A}_{4}$,
$\mathbb{A}_{5}$ or $\mathbb{A}_{6}$ are K\"ahler-Einstein.
