4 problems

Let $X$ and $X'$ be birationally equivalent terminal Fano varieties of dimension $3$ and Picard rank one over $\mathbb{C}$. A birational map $f\colon X\dashrightarrow X'$ is said t…

Strong Sarkisov program. The sequence of Sarkisov links constructed in the strong Sarkisov link construction terminates. Equivalently, the birational map…

Let $d$ be an integer with $1\leq d\leq 3$. Let $X\to\mathbb P^1$ be a $\mathfrak D$-semistable del Pezzo fibration of degree $d$, and assume that it satisfies the $K$-condition, m…

Let $X$ be a smooth threefold Mori fibre space over $\mathbb{P}^1$, with fibres being smooth del Pezzo surfaces of degree $4$. Let $\operatorname{Mob}(X)$ denote the mobile cone of…