12-17【Junsheng Zhang】On Kähler-Ricci shrinkers and polarized Fano fibration

We prove that every Kähler-Ricci shrinker (not necessarily compact) admits a quasi-projective variety structure. The proof uses Kähler reduction and Birkar's boundedness result for Fano varieties. Moreover we propose several conjectures for Kähler-Ricci shrinkers, which unifies the well-developed theories for Kähler-Einstein metrics and Calabi-Yau cones.