Rank jumps and Multisections of elliptic fibrations on K3 surfaces

Alice Garbagnati, Cecília Salgado

We consider the countably many families ${\mathcal{L}}_d$, $d\in {\mathbb{N}}_{\ge 2}$, of K3 surfaces admitting an elliptic fibration with positive Mordell--Weil rank. We prove that t…