IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-92297-8_1.html
   My bibliography  Save this book chapter

From Kähler Ricci Solitons to Calabi-Yau Kähler Cones

In: Real and Complex Geometry

Author

Listed:
  • Vestislav Apostolov

    (Département de Mathématiques, UQAM, C.P. 8888
    Bulgarian Academy of Sciences, Institute of Mathematics and Informatics)

  • Abdellah Lahdili

    (Département de Mathématiques, UQAM, C.P. 8888)

  • Eveline Legendre

    (Institut Camille Jordan équipe AGL, Université Claude Bernard Lyon 1)

Abstract

We show that if X is a smooth Fano manifold which carries a Kähler Ricci soliton, then the canonical cone of the product of X with a complex projective space of sufficiently large dimension is a Calabi–Yau cone, i.e. admits a Ricci-flat Kähler cone metric. This can be seen as an asymptotic version of a conjecture by Mabuchi and Nikagawa. This result is obtained by the relative openness of the set of weight functions v over the momentum polytope of a given smooth Fano manifold, for which a v-soliton exists. We discuss other ramifications of this approach, including a Licherowicz type obstruction to the existence of a Kähler Ricci soliton and a Fujita type volume bound for the existence of a v-soliton.

Suggested Citation

  • Vestislav Apostolov & Abdellah Lahdili & Eveline Legendre, 2025. "From Kähler Ricci Solitons to Calabi-Yau Kähler Cones," Springer Books, in: Liviu Ornea (ed.), Real and Complex Geometry, pages 1-40, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-92297-8_1
    DOI: 10.1007/978-3-031-92297-8_1
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-92297-8_1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.