Paper · Jun 26, 2017

Kähler-Ricci solitons on some wonderful group compactifications

François Delgove

math.DGarXiv:1706.08285v3
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Abstract

In this paper, we extend the result about the existence of Kähler-Ricci soliton on toric manifold (proved by Wang and Zhy) by proving this existence on some wonderful group compactifications using the continuity method.

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Submitted
Jun 26, 2017
Last revised
Feb 15, 2019 (v3)
Subjects
math.DG

Comments: Error in computation of Futaki Invariant

Ricci solitonsKähler–Ricci solitonsKähler geometry

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Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Kähler-Ricci solitons on horospherical variety (François Delgove, 2017)1Delgove 2017 Kähler-Ricci flow on horospherical manifold (François Delgove, 2019)2Delgove 2019 Existence and uniqueness of S¹-invariant Kähler-Ricci solitons (Johannes Schäfer, 2020)5Schäfer 2020 Uniqueness of shrinking gradient Kähler-Ricci solitons on non-compact toric manifolds (Charles Cifarelli, 2020)4Cifarelli 2020 Lower bound of modified K-energy on a Fano manifold with degeneration for Kähler-Ricci solitons (Liang Zhang, 2021)6Zhang 2021 Toric geometry of generalized Kähler-Ricci solitons (Vestislav Apostolov, Giuseppe Barbaro, Jeffrey Streets et al., 2025)3Apostolov 2025 An Aubin continuity path for asymptotically conical toric shrinking gradient Kähler-Ricci solitons: openness and a solution for t=0 (Ivin Babu, Ronan J. Conlon and Alix Deruelle, 2025)7Babu 2025 Uniqueness of the soliton vector field of a shrinking gradient Kähler-Ricci soliton (Ronan J. Conlon and Alix Deruelle, 2026)8Conlon 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Kähler-Ricci solitons on horospherical variety

    François Delgove

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same author François Delgove · Shared terms “toric manifold”, “Zhy”, “continuity”

  2. Kähler-Ricci flow on horospherical manifold

    François Delgove

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same author François Delgove

  3. Toric geometry of generalized Kähler-Ricci solitons

    Vestislav Apostolov, Giuseppe Barbaro, Jeffrey Streets et al.

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons

  4. Uniqueness of shrinking gradient Kähler-Ricci solitons on non-compact toric manifolds

    Charles Cifarelli

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “toric manifold”

  5. Existence and uniqueness of -invariant Kähler-Ricci solitons

    Johannes Schäfer

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons

  6. Lower bound of modified -energy on a Fano manifold with degeneration for Kähler-Ricci solitons

    Liang Zhang

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons

  7. An Aubin continuity path for asymptotically conical toric shrinking gradient Kähler-Ricci solitons: openness and a solution for

    Ivin Babu, Ronan J. Conlon and Alix Deruelle

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “continuity”

  8. Uniqueness of the soliton vector field of a shrinking gradient Kähler-Ricci soliton

    Ronan J. Conlon and Alix Deruelle

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Kähler–Ricci solitons Kähler metrics whose Ricci form differs from the metric by a Lie derivative along a holomorphic vector field. Start with: Uniqueness of Kähler-Ricci solitons (Tian et al., 2000) Kähler geometry Complex manifolds with compatible Riemannian metrics whose Kähler form is closed. Here Ricci curvature is the complex Hessian of a log-determinant… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978)

In the guidebook

  1. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

  2. 12B.2
    The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery

    Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.