MMP on the generic fiber of log Calabi--Yau type fibration

2025/12/02 by Donghyeon Kim, Kim, Donghyeon, Dae-Won Lee +1
Mathematics · #14E05 #14E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2512.02429

openalex publication_date 2025/12/02 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/30

Abstract

We study the minimal model program on the geometric generic fiber of a fibration whose closed fibers are of ε-lc log Calabi--Yau type. We prove that for a fibration f:X→ S of varieties, if the fibers are of ε-lc log Calabi--Yau type, then the geometric generic fiber X_η is pklt. In particular, for any big divisor D on X_η, we can run the anticanonical MMP and D-MMP with scaling of an ample divisor on X_η.

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