Kähler-Ricci Shrinkers and Polarized Fano Fibrations

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Junsheng Zhang, NYU
Fine Hall 314

We prove that every (non-compact) Kähler-Ricci shrinker is naturally a polarized Fano fibration. The proof relies on Kähler reductions and Birkar’s boundedness result in birational geometry. Moreover, we propose several conjectures for Kähler-Ricci shrinkers, unifying the well-developed theories of Kähler-Einstein metrics and Calabi-Yau cones. This is joint work with Song Sun.