A smooth cubic surface contains 27 lines, but a singular cubic surface with rational double points contains fewer lines.
Question: Why is the number of lines equal to $\binom{8-r}{2}+n-1$, where $r$ is the total number of points in the Dynkin diagrams of the singularities, and $n$ the number of singularities? Is there a similar formula for other del Pezzo surfaces?
Example. Consider the case $A_{1}A_{4}$. The total number of points is $5$ and there are $2$ singularities, so the number of lines equals $\binom{8-5}{2}+2-1=4$.