Holomorphic fibrations on Calabi-Yau manifolds and collapsing

Consider a compact Calabi-Yau manifolds with a holomorphic fibration onto a lower-dimensional base. Pulling back a Kahler class from the base, we obtain a class on the boundary of the Kahler cone, which is a limit of Kahler classes. These classes contain Ricci-flat metrics, which in the limit collapse to a twisted Kahler-Einstein metric on the base (away from the singular fibers). Furthermore if we rescale so that the fibers have fixed size, then away from the singular fibers the limit is a cylinder over a Ricci-flat fiber. This is based on joint work with Weinkove and Yang, with Hein and with Zhang, and is directly related to the topic of the talk by Mark Gross

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