Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones

2026/07/28 by Ronan J. Conlon, Alix Deruelle
#math.DG

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Abstract

We show that any complete shrinking gradient Kähler-Ricci soliton on a resolution of a Kähler cone is necessarily asymptotically conical. From a result of Esparza, it then follows that up to pullback by biholomorphism, there exists at most one complete shrinking gradient Kähler-Ricci soliton on such a resolution. This confirms a special case of the uniqueness part of a conjecture of Song-Zhang. Some other consequences are also discussed.

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