Kähler-Ricci Shrinkers and Polarized Fano Fibrations

Date
2025/10/15 Wed 16:00 - 17:00
Speaker
Junsheng Zhang
Affiliation
Courant Institute
Abstract

We prove that every Kähler-Ricci shrinker i.e., complete Kahler-Ricci soliton naturally admits a polarized Fano fibration structure. The proof relies on symplectic reductions and Birkar’s boundedness results 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.