7 problems

Effective Iitaka fibration conjecture. There exists a positive integer $m_d$ depending only on $d$, such that for every smooth projective variety $X$ of dimension $d$ with non-nega…

Decomposable Iitaka fibration conjecture. There exist a positive integer $m$, a finite set $\Gamma_0\subset(0,1]$, and a DCC set $\Gamma'\subset[0,1]$, depending only on $d$ and…

Decomposable Iitaka fibration conjecture. There exist a positive integer $m$, a finite set $\Gamma_0\subset(0,1]$, and a DCC set $\Gamma'\subset[0,1]$, depending only on $d$ and…

Effective log Iitaka fibration conjecture. There exists a positive integer $m$ depending only on $d$ and $\tau$ such that, whenever $(X,B)$ is an lc pair of dimension $d$ with $B$…

Let $n$ be a positive integer, let $v$ be a non-negative rational number, and let $cmathcal{I}subset [0,1]cap cmathbb{Q}$ be a DCC set of rational numbers. For a klt pair…

Boundedness conjecture. The set of all such varieties $Z$ is a bounded family.

Let $W$ be a smooth projective variety of dimension $d$ with Kodaira dimension $\kappa(W)\ge 0$. An Iitaka fibration of $W$ is the fibration, defined up to birational equivalence,…