 Blowup of affine space at the origin

The blowup of ${\mathbb{A}}^n$ at the origin is the total space of the tautological line bundle ${\mathcal{O}}_{{\mathbb{P}}^{n-1}}(-1)$. Its exceptional divisor is the zero section ${\mathbb{P}}^{n-1}$, and projection to the direction of a line gives the bundle map to ${\mathbb{P}}^{n-1}$.