Paper · Nov 6, 2017

Steady Kähler-Ricci solitons on crepant resolutions of finite quotients of

Olivier Biquard, Heather Macbeth

math.DGarXiv:1711.02019
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As on arXiv

Abstract

We prove the existence of steady Kähler-Ricci solitons on equivariant crepant resolutions of , where is a finite subgroup of .

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Submitted
Nov 6, 2017
Subjects
math.DG
Ricci solitonsKähler–Ricci solitonsKähler geometry

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  1. Steady gradient Kähler-Ricci solitons on crepant resolutions of Calabi-Yau cones

    Ronan J. Conlon and Alix Deruelle

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “crepant resolutions”, “equivariant crepant”

  2. Asymptotically cylindrical steady Kähler-Ricci solitons

    Johannes Schäfer

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “steady Kähler”, “crepant resolutions”

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

    Johannes Schäfer

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

  4. The asymptotic behavior of the steady gradient Kähler-Ricci soliton of the Taub-NUT type of Apostolov and Cifarelli

    Daheng Min

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “crepant resolutions”, “quotient”

  5. Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones

    Ronan J. Conlon and Alix Deruelle

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

  6. Gradient steady Kahler Ricci solitons with non-negative Ricci curvature and integrable scalar curvature

    Pak-Yeung Chan

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

  7. Liouville type theorems for harmonic functions on gradient Ricci solitons

    Yong Luo

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

  8. On geometry of steady toric Kähler-Ricci solitons

    Yury Ustinovskiy

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

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.