Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 4, pp. 919-934.

On donne un critère pour la coercivité de la fonctionnelle de Mabuchi pour des classes de Kähler générales sur les variétés de Fano en termes d’invariant alpha de Tian. Cela généralise un théorème de Tian dans le cas anticanonique, ce qui implique l’existence d’une métrique Kähler-Einstein. On montre également que l’invariant alpha est une fonction continue sur le cône de Kähler. On en déduit de nouvelles classes de Kähler sur des surfaces de Del Pezzo pour lesquelles la fonctionnelle de Mabuchi est coercive.

We give a criterion for the coercivity of the Mabuchi functional for general Kähler classes on Fano manifolds in terms of Tian’s alpha invariant. This generalises a result of Tian in the anti-canonical case implying the existence of a Kähler-Einstein metric. We also prove the alpha invariant is a continuous function on the Kähler cone. As an application, we provide new Kähler classes on a general degree one del Pezzo surface for which the Mabuchi functional is coercive.

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     author = {Dervan, Ruadha{\'\i}},
     title = {Alpha invariants and coercivity of the {Mabuchi} functional on {Fano} manifolds},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {919--934},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 25},
     number = {4},
     year = {2016},
     doi = {10.5802/afst.1515},
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Dervan, Ruadhaí. Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 4, pp. 919-934. doi : 10.5802/afst.1515. http://archive.numdam.org/articles/10.5802/afst.1515/

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