The study demonstrates the termination of a minimal model program in normal pairs, highlighting implications for the abundance conjecture.
Let (X,Δ ) be a normal pair with a projective morphism X → Z and let A be a relatively ample R -divisor on X . We prove the termination of some minimal model program on (X,Δ +A)/Z and the abundance conjecture for its minimal model under assumptions that the non-nef locus of KX+Δ +A over Z does not intersect the non-lc locus of (X,Δ ) and that the restriction of KX+Δ +A to the non-lc locus of (X,Δ ) is semi-ample over Z .
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Kenta Hashizume (2025) studied this question.
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