Geometry of twisted Kahler-Einstein metrics and collapsing

Mark Gross, Valentino Tosatti, Yuguang Zhang

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
JournalUnknown Journal
StatePublished - Nov 17 2019

ASJC Scopus subject areas

  • General

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