Relative tautological line bundle
= Relative tautological line bundle
{title2=$S_\ell=\ell,\quad S\subset p^*E$}
On the <holomorphic projectivization by lines>, take the line itself as the fibre of $S$. The evaluation inclusion makes it a holomorphic line subbundle of $p^*E$. Its fibre restriction is $\mathcal O(-1)$; the dual is the <relative hyperplane line bundle>.