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arXiv · 1911.07315

Geometry of twisted K\"ahler-Einstein metrics and collapsing

Mark Gross·Valentino Tosatti·Yuguang Zhang
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Abstract

We prove that the twisted Kahler-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 Kahler metrics on Calabi-Yau manifolds, and of the Kahler-Ricci flow on compact Kahler 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.

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Mark Gross, Valentino Tosatti, Yuguang Zhang. 2019-11-17. Geometry of twisted K\"ahler-Einstein metrics and collapsing. https://doi.org/10.1007/s00220-020-03911-0

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