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arXiv · 2310.13904

Minimal model program for normal pairs along log canonical locus

Kenta Hashizume
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Abstract

Let $(X,\Delta)$ be a normal pair with a projective morphism $X \to Z$ and let $A$ be a relatively ample $\mathbb{R}$-divisor on $X$. We prove the termination of some minimal model program on $(X,\Delta+A)/Z$ and the abundance conjecture for its minimal model under assumptions that the non-nef locus of $K_{X}+\Delta+A$ over $Z$ does not intersect the non-lc locus of $(X,\Delta)$ and that the restriction of $K_{X}+\Delta+A$ to the non-lc locus of $(X,\Delta)$ is semi-ample over $Z$.

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Kenta Hashizume. 2023-10-21. Minimal model program for normal pairs along log canonical locus. https://doi.org/10.1017/fms.2025.10092

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