K-stable smoothable Q-Fano varieties admit Kähler-Ricci solitons, extending the Yau-Tian-Donaldson correspondence for solitons from the smooth case to the singular smoothable case.
Geometric pluripotential theory on K\"ahler manifolds
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abstract
Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Amp\`ere type arising in K\"ahler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, effectively turning the variational problems in question into problems of infinite dimensional convex optimization, yielding existence results for solutions of the underlying complex Monge-Amp\`ere equations. The purpose of this survey is to describe these developments from basic principles.
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Existence of Kahler-Ricci solitons on smoothable Q-Fano varities
K-stable smoothable Q-Fano varieties admit Kähler-Ricci solitons, extending the Yau-Tian-Donaldson correspondence for solitons from the smooth case to the singular smoothable case.