K-stability of Fano threefolds of rank 4 and degree 24. (English) Zbl 1535.14093
The existence of Kähler-Einstein metric on Fano varieties is obstructed, unlike the case of Calabi-Yau or varieties of general type. By the Yau-Tian-Donaldson correspondence, the existence of such metric is equivalent to K-polystability of the Fano variety. The latter can be verified by an inductive method due to Abban and Zhuang.The authors successfully apply this method to Fano varieties given as smooth hypersurfaces of degree \((1,1,1,1)\) in \(\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\).
Reviewer: Hamid Abban (Nottingham)
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