The effective Iitaka fibration conjecture

Theorem 1.1: for each $d\ge1$ there is $m(d)>0$ such that, over every algebraically closed field of characteristic zero, $|m(d)K_X|$ is nonempty and its section ratios generate the Iitaka function field for every smooth integral projective $d$-fold with $\kappa(X)\ge0$; every multiple of $m(d)$ works too. Theorem 1.2 gives a uniform $a(d,\Phi)$ with $a(K_X+B)\sim0$ for projective lc pairs with $K_X+B\sim_{\mathbb Q}0$ and coefficients in a DCC set $\Phi$. The bound $m(d)$ is existential; no explicit value is given.

This result uses the release's log abundance theorem as an input, and the release contradicts itself on whether that theorem is unconditional (24 September abstract) or a conditional resolution resting on logarithmic Iitaka subadditivity (5 October appendix). The entry is Contested with it. Theorem 1.1: for each $d\ge1$ there is $m(d)>0$ such that, over every algebraically closed field of characteristic zero, $|m(d)K_X|$ is nonempty and its section ratios generate the Iitaka function field for every smooth integral projective $d$-fold with $\kappa(X)\ge0$; every multiple of $m(d)$ works too. Theorem 1.2 gives a uniform $a(d,\Phi)$ with $a(K_X+B)\sim0$ for projective lc pairs with $K_X+B\sim_{\mathbb Q}0$ and coefficients in a DCC set $\Phi$. The bound $m(d)$ is existential; no explicit value is given.