Universal quotient line bundle
= Universal quotient line bundle
{title2=$\pi^*E\twoheadrightarrow\mathcal O_{\mathbb P(E)}(1)$}
On the <projectivization by quotients>, the fibre over a one-dimensional quotient of $E_x$ is that quotient line itself. These lines glue to the universal quotient. Its restriction to a projective fibre has degree one. It is the dual of the relative tautological line after identifying quotient projectivization of $E$ with line projectivization of $E^*$.