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Mathematics > Differential Geometry

arXiv:1805.03084 (math)
[Submitted on 8 May 2018]

Title:Compactness of Kahler-Ricci solitons on Fano manifolds

Authors:Bin Guo, Duong H. Phong, Jian Song, Jacob Sturm
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Abstract:In this short paper, we improve the result of Phong-Song-Sturm on degeneration of Fano Kähler-Ricci solitons by removing the assumption on the uniform bound of the Futaki invariant. Let $\mathcal{KR}(n)$ be the space of Kähler-Ricci solitons on $n$-dimensional Fano manifolds. We show that after passing to a subsequence, any sequence in $\mathcal{KR}(n)$ converge in the Gromov-Hausdorff topology to a Kähler-Ricci soliton on an $n$-dimensional $\mathbb{Q}$-Fano variety with log terminal singularities.
Comments: 10 pages
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:1805.03084 [math.DG]
  (or arXiv:1805.03084v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1805.03084

Submission history

From: Bin Guo [view email]
[v1] Tue, 8 May 2018 15:02:48 UTC (10 KB)
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