Sections and Unirulings of Families over $\mathbb{P}^{1}$
Sections and Unirulings of Families over $\mathbb{P}^{1}$
Abstract We consider morphisms $\pi : X \to \mathbb{P}^{1}$ of smooth projective varieties over $\mathbb{C}$ . We show that if π has at most one singular fibre, then X is uniruled and π admits sections. We reach the same conclusions, but with genus zero multisections instead of sections, if π …