We prove that the twisted Kähler-Einstein metrics that arise on the base of certain holomorphic fiber space with Calabi-Yau fibers have conical-type singularities along the discriminant locus. These fiber spaces arise naturally when studying the collapsing of Ricci-flat Kähler metrics on Calabi-Yau manifolds, and of the Kähler-Ricci flow on compact Kähler manifolds with semiample canonical bundle and intermediate Kodaira dimension. Our results allow us to understand their collapsed Gromov-Hausdorff limits when the base is smooth and the discriminant has simple normal crossings.
MSC Codes 32Q25, 32Q20, 32W20, 14J32, 53C25
|Original language||English (US)|
|State||Published - Nov 17 2019|
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