Minimal model program for normal pairs along log canonical locus

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 $Z$.

Final version, 79 pages. Expositions in the introduction were improved. Some properties on relative Nakayama--Zariski decomposition were added. Other minor changes were done. To appear in Forum Math. Sigma

References in corpus (6)

• The diminished base locus is not always closed
• On Generalised Abundance, I
• Special MMP for log canonical generalised pairs
• Semi-ampleness of NQC generalized log canonical pairs
• Iitaka fibrations for dlt pairs polarized by a nef and log big divisor
• Remarks on the existence of minimal models of log canonical generalized pairs

Cited by in corpus (1)

• Remarks on the minimal model theory for log surfaces in the analytic setting