June 2020 Expanding Kähler–Ricci solitons coming out of Kähler cones
Ronan J. Conlon, Alix Deruelle
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J. Differential Geom. 115(2): 303-365 (June 2020). DOI: 10.4310/jdg/1589853627


We give necessary and sufficient conditions for a Kähler equivariant resolution of a Kähler cone, with the resolution satisfying one of a number of auxiliary conditions, to admit a unique asymptotically conical (AC) expanding gradient Kähler–Ricci soliton. In particular, it follows that for any $n \in \mathbb{N}_0$ and for any negative line bundle $L$ over a compact Kähler manifold $D$, the total space of the vector bundle $L^{\oplus (n+1)}$ admits a unique AC expanding gradient Kähler–Ricci soliton with soliton vector field a positive multiple of the Euler vector field if and only if $c_1 \Bigl ( K_D \oplus {(L^\ast)}^{\oplus (n+1)} \Bigr ) \gt 0$. This generalizes the examples already known in the literature. We further prove a general uniqueness result and show that the space of certain AC expanding gradient Kähler–Ricci solitons on $\mathbb{C}^n$ with positive curvature operator on $(1, 1)$-forms is path-connected.


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Ronan J. Conlon. Alix Deruelle. "Expanding Kähler–Ricci solitons coming out of Kähler cones." J. Differential Geom. 115 (2) 303 - 365, June 2020. https://doi.org/10.4310/jdg/1589853627


Received: 26 September 2016; Published: June 2020
First available in Project Euclid: 19 May 2020

zbMATH: 07210962
MathSciNet: MR4100705
Digital Object Identifier: 10.4310/jdg/1589853627

Rights: Copyright © 2020 Lehigh University


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Vol.115 • No. 2 • June 2020
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