Title: On the cone conjecture for log Calabi-Yau threefolds.Abstract: Let $Y$ be a smooth projective threefold admitting a $K3$ fibration $f: Y rightarrow mathbb{P}^{1}$ with $-K_{Y} = f^{ast} mathcal{O}(1)$. Then the extremal rays of the cone of curves of $Y$ in the region $K_{Y} < 0$ are of two types: the blowup of a smooth curve (Type […]