Abstract
AbstractAs a generalization of Kähler–Einstein metrics for Fano manifolds with nonvanishing Futaki invariant, Mabuchi solitons are critical points of a Calabi-type energy functional. We study their existence on toric Fano varieties and the underlying algebraic stability notion: relative Ding stability. As a toy model for a YTD type correspondence, a new feature is the emergence of a nonuniformly stable case. We show a partial coercivity for the modified Ding functionals in this case and obtain singular Mabuchi solitons via a variational approach. In the unstable case, we determine the maximal destabilizer, which is a simple convex function over the moment polytope, and establish a moment–weight equality that connects the infimum of a Calabi-type energy and the Berman–Ding invariant.
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