The effective log Iitaka conjecture for log canonical pairs with finite rational coefficient sets

'Uniform effective log Iitaka fibrations for fourfolds' (September 26): for normal projective lc complex fourfolds with coefficients in a fixed finite rational set and pseudo-effective rational Cartier adjoint, one degree makes the rounded system nonempty with section ratios generating the Iitaka field; it also bounds the canonical index of klt Calabi-Yau fourfolds. 'Uniform log Iitaka fibrations and bounded moduli denominators' (October 4): the same conclusion for $d\ge5$ over any algebraically closed field of characteristic zero, with bounded Cartier denominators for moduli divisors. Not shown: the DCC case of the conjecture in dimension four or more.

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. 'Uniform effective log Iitaka fibrations for fourfolds' (September 26): for normal projective lc complex fourfolds with coefficients in a fixed finite rational set and pseudo-effective rational Cartier adjoint, one degree makes the rounded system nonempty with section ratios generating the Iitaka field; it also bounds the canonical index of klt Calabi-Yau fourfolds. 'Uniform log Iitaka fibrations and bounded moduli denominators' (October 4): the same conclusion for $d\ge5$ over any algebraically closed field of characteristic zero, with bounded Cartier denominators for moduli divisors. Not shown: the DCC case of the conjecture in dimension four or more.