 Isotropic divisor from a nontrivial birational morphism to the projective plane

Every nonisomorphic birational morphism from a smooth projective surface to ${\mathbb{P}}^2$ factors into point blowups. If $H$ is the pullback of a line and $E$ is the total transform of an exceptional divisor from one factor, then $H^2=1$, $E^2=-1$ and $H\cdot E=0$, so $(H+E{)}^2=0$.