3 problems

Let $\pi:\mathcal{X}\longrightarrow\Delta$ be a holomorphic family of compact Kähler manifolds $X_t:=\pi^{-1}(t)$ over the open unit disc $\Delta\subset\mathbb{C}$. For a positive…

Effective pluricanonicality conjecture. Assume $\kappa(W)\geq 0$. Then there exists $m\in\mathbb N$ depending only on $\dim W$ such that $|mK_W|$ defines the Iitaka fibration.

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,…