Relative tautological line bundle ($S_{\ell }=\ell ,S\subset p^{\ast }E$)

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 $p^{\ast }E$. Its fibre restriction is $\mathcal{O}(-1)$; the dual is the relative hyperplane line bundle.

Dualize the relative tautological line bundle to obtain the positive relative hyperplane line bundle. It restricts to $\mathcal{O}(1)$ on each projective fibre. This sign depends on the convention that projectivization parametrizes lines; fixing the convention avoids confusing it with the tautological line itself.