3 problems

Let $R\to\mathbb P^1$ be a rational elliptic surface, let $L$ determine a Severi curve with normalization $\widetilde{V}(L)$, and let…

Let $R\to\mathbb P^1$ be a general rational elliptic surface, and let sections mean section curves of this elliptic fibration. Transversality conjecture. Any two sections meet tran…

Let $R$ be a rational elliptic surface, and let $V(R,L)$ denote the genus $0$ Severi variety associated to a line bundle $L$ on $R$. Reducibility conjecture. There exist line bundl…