From Kähler Ricci Solitons to Calabi-Yau Kähler Cones

Vestislav Apostolov (), Abdellah Lahdili and Eveline Legendre ()
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Vestislav Apostolov: Département de Mathématiques, UQAM, C.P. 8888
Abdellah Lahdili: Département de Mathématiques, UQAM, C.P. 8888
Eveline Legendre: Institut Camille Jordan équipe AGL, Université Claude Bernard Lyon 1

A chapter in Real and Complex Geometry, 2025, pp 1-40 from Springer

Abstract: 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.

Keywords: Calabi-Yau; Sasaki-Einstein; v-Soliton; Weighted cscK; Kahler-Ricci solitons (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-92297-8_1

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DOI: 10.1007/978-3-031-92297-8_1

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