The effective Iitaka fibration conjecture

Lineage and corrections

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. parent of this event

Revised edition (October 6, 2026): Conditional good minimal models for compact Kähler fourfolds evidence for this event

Birkar and Zhang (2016), Conjecture 1.1 evidence for this event

VibeMathed record: The effective Iitaka fibration conjecture evidence for this event

Input manuscript: Log abundance in characteristic zero evidence for this event

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The effective Iitaka fibration conjecture parent of this event

The 5 October appendix calling projective log abundance conditional evidence for this event

Input: Uniform Pluricanonical Iitaka Fibrations (normal lc index, DCC) evidence for this event