Compactness of Kähler–Ricci solitons on Fano manifolds

Bin Guo, Duong H. Phong, Jian Song, Jacob Sturm

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In this short paper, we improve the result of Phong– Song–Sturm on degeneration of Fano Kähler–Ricci solitons by re-moving the assumption on the uniform bound of the Futaki in-variant. Let KR(n) be the space of Kähler–Ricci solitons on n-dimensional Fano manifolds. We show that after passing to a subse-quence, any sequence in KR(n) converge in the Gromov–Hausdorff topology to a Kähler–Ricci soliton on an n-dimensional Q-Fano va-riety with log terminal singularities.

Original languageEnglish (US)
Pages (from-to)305-316
Number of pages12
JournalPure and Applied Mathematics Quarterly
Issue number1
StatePublished - 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Fano manifolds
  • Kähler-Ricci solitons


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