Minimal model program on the generic fiber of log Calabi-Yau type fibration

Paper

Abstract

We study the minimal model program on the geometric generic fiber of a fibration

such that for a Zariski dense subset

is an

-lc log Calabi--Yau type for every

. We prove that for a fibration

of varieties, if the fibers are of

-lc log Calabi--Yau type, then the geometric generic fiber

is pklt. In particular, for any big divisor

, we can run the anticanonical MMP and

-MMP with scaling of an ample divisor on