3 problems

Mori structures conjecture. The Mori structures of $U$ are precisely $U$ itself and

Classification conjecture. Any smooth Mori fibration birational to $U$ is biregular to either $U$ or $V_l$ for some curve $l$.

A Sarkisov link is a birational map, or birational cobordism, connecting two Mori fibrations. Landau–Ginzburg families conjecture. One-parameter families of Landau–Ginzburg models…