9 problems

Let $(X,\Delta)$ be a Klt pair, and let $f:X\to Y$ be an algebraic fiber space, where $X$ and $Y$ are smooth projective varieties of dimensions $n$ and $m$, respectively. Let $F$ b…

Let $f\colon X\to Y$ be an algebraic fiber space between smooth projective varieties, and let $F$ be its general fiber with $\kappa(F)=0$. Suppose that there are an ample divisor…

Let $f:X\to Y$ be an algebraic fiber space between smooth projective varieties, and suppose that the general fiber $F$ satisfies $\kappa(F)=0$. Let $H$ be an ample divisor on $Y$.…

Let $f:X\to Y$ be an algebraic fiber space, meaning that $X$ and $Y$ are smooth projective varieties and $f$ is surjective with connected fibers. Let $F$ be a generic fiber satisfy…

Let $f\colon X\to Y$ be an algebraic fiber space between smooth projective varieties. Let $E$ be a simple normal crossing divisor on $X$ and $D$ a simple normal crossing divisor on…

Let $f\colon U\to V$ be a smooth projective algebraic fiber space between smooth quasi-projective varieties, and let $F$ be its general fiber. The quasi-projective additivity conje…

Let $f\colon X\to Y$ be a smooth algebraic fiber space between smooth projective varieties, and let $F$ be its general fiber. The additivity conjecture. One should have … This foll…

The superadditivity conjecture. One should have

Iitaka–Viehweg conjecture. The Kodaira dimension of $X$ satisfies