The index conjecture for semi-log-canonical log Calabi-Yau pairs with finite rational coefficient sets

Theorem 1.1: for every $d\ge4$ and finite $\Phi\subset[0,1]\cap\mathbb Q$ there is $a(d,\Phi)>0$ such that $a(d,\Phi)(K_X+B)$ is Cartier with trivial line bundle for every connected projective equidimensional slc log Calabi-Yau pair of dimension $d$ with coefficients in $\Phi$, independently of the number of components. With Jiang-Liu's theorem for $d\le3$ this gives the conjecture in the cited form. Not shown: slc pairs with infinite DCC coefficient sets, or explicit values of $a(d,\Phi)$.

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 every $d\ge4$ and finite $\Phi\subset[0,1]\cap\mathbb Q$ there is $a(d,\Phi)>0$ such that $a(d,\Phi)(K_X+B)$ is Cartier with trivial line bundle for every connected projective equidimensional slc log Calabi-Yau pair of dimension $d$ with coefficients in $\Phi$, independently of the number of components. With Jiang-Liu's theorem for $d\le3$ this gives the conjecture in the cited form. Not shown: slc pairs with infinite DCC coefficient sets, or explicit values of $a(d,\Phi)$.