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Non-reductive automorphism groups, the Loewy filtration and K-stability
(l'Institut FourierAnnales de l'Institut Fourier, 2016-03-18)
We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several ...
Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
(Université Paul SabatierAnnales de la Faculté des Sciences de Toulouse, 2016)
We give a criterion for the coercivity of the Mabuchi functional for general Kàhler classes on Fano manifolds in terms of Tian's alpha invariant. This generalises a result of Tian in the anti-canonical case implying the ...
On K-stability of finite covers
(Oxford University PressJournal of the London Mathematical Society, 2016)
We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting Kähler-Einstein metrics, including hypersurfaces, double solids and threefolds.