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.

中文翻译：

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扭曲 Kähler-Einstein 度量和折叠的几何

我们证明了在具有 Calabi-Yau 纤维的某些全纯纤维空间的基础上出现的扭曲的 Kahler-Einstein 度量具有沿着判别轨迹的锥形奇点。这些纤维空间是在研究 Calabi-Yau 流形上的 Ricci-flat Kahler 度量的塌缩和具有半宽规范丛和中间 Kodaira 维的紧凑 Kahler 流形上的 Kahler-Ricci 流的坍缩时自然出现的。我们的结果使我们能够理解当基础平滑且判别式具有简单的法线交叉时，它们的崩溃 Gromov-Hausdorff 极限。