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arXiv · 2407.01871

Mabuchi K\"ahler solitons versus extremal K\"ahler metrics and beyond

Vestislav Apostolov·Abdellah Lahdili·Yasufumi Nitta
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Abstract

Using the Yau-Tian-Donaldson type correspondence for $v$-solitons established by Han-Li, we show that a smooth complex $n$-dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal K\"ahler metric whose scalar curvature is strictly less than $2(n+1)$. Combined with previous observations by Mabuchi and Nakamura in the other direction, this gives a characterization of the existence of Mabuchi solitons in terms of the existence of extremal K\"ahler metrics on Fano manifolds. An extension of this correspondence to $v$-solitons is also obtained.

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Vestislav Apostolov, Abdellah Lahdili, Yasufumi Nitta. 2024-07-02. Mabuchi K\"ahler solitons versus extremal K\"ahler metrics and beyond. https://arxiv.org/abs/2407.01871

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