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.
Degenerations of K\"ahler-Einstein Fano Manifolds
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In this Thesis, I investigate how Fano manifolds equipped with a Kahler-Einstein metric can degenerate as metric spaces (in the Gromov-Hausdorff topology) and some of the relations of this question with Algebraic Geometry, in particular in the direction of the study of moduli spaces and their compactifications.
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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.