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arXiv · 2607.26054

Uniqueness of shrinking K\"ahler-Ricci solitons on resolutions of K\"ahler cones

Ronan J. Conlon·Alix Deruelle
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Abstract

We show that any complete shrinking gradient K\"ahler-Ricci soliton on a resolution of a K\"ahler 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 K\"ahler-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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Ronan J. Conlon, Alix Deruelle. 2026-07-28. Uniqueness of shrinking K\"ahler-Ricci solitons on resolutions of K\"ahler cones. https://arxiv.org/abs/2607.26054

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