I think there was a theorem, like 


* every cubic hypersurface in $\mathbb P^3$ has 27 lines on it.


What is the exact statement and details?



What is the exact statement of "there are 27 lines on a cubic"?
The exact statement is that every smooth cubic surface in $\mathbb P^3$ (over an algebraically closed field) has exactly $27$ lines on it. Many books on algebraic geometry include a proof of this famous fact. The proof that I first learned comes from chapter V of Hartshorne, where cubic surfaces arise as the blowup of $\mathbb P^2$ at $6$ points, and where the formula $27=6+15+6$ is explained.


