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

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

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

VibeMathed record: The index conjecture for semi-log-canonical log Calabi-Yau pairs with finite rational coefficient sets evidence for this event

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

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 $a(d,\Phi)$. 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

Jiang and Liu, Boundedness of log pluricanonical representations (arXiv 2002.11928), Conjecture 1.5 evidence for this event