Shokurov’s local index conjecture for threefolds

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AI-generated paper · posted here 2026-10-13 14:23:44 UTC · not submitted to arXiv · permanent link: jihaoliu.org/papers/shokurovs-local-index-conjecture-for-threefolds.html

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We prove Shokurov’s local index conjecture in dimension three: for every positive real number a there is a positive integer R₃(a) such that, for every klt threefold germ X ∋ x with mld(X ∋ x) = a, the divisor R₃(a)K_X is Cartier near x. More generally, for every finite set Γ of rational numbers in [0,1] there is a positive integer R₃(a,Γ) such that R₃(a,Γ)(K_X + B) is Cartier near x for every klt threefold germ (X ∋ x, B) with the coefficients of B in Γ and mld(X ∋ x, B) = a.

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