On a connectedness principle of Shokurov-Kollár type
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摘要:
Let (X,△) be a log pair over S,such that-(Kx + △) is nef over S.It is conjectured that the intersection of the non-klt (non Kawamata log terminal) locus of (X,△) with any fiber Xs has at most two connected components.We prove this conjecture in dimension no greater than 4 and in arbitrary dimension assuming the termination of klt flips.