Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds
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Peer-reviewed
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Authors
Dervan, Ruadhaí
Abstract
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 existence of a Kàhler-Einstein metric. We also prove the alpha invariant is a continuous function on the Kàhler cone. As an application, we provide new Kàhler classes on a general degree one del Pezzo surface for which the Mabuchi functional is coercive.
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Journal Title
Annales de la Faculté des Sciences de Toulouse
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Journal ISSN
0240-2963
2258-7519
2258-7519
Volume Title
25
Publisher
Université Paul Sabatier
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Sponsorship
Engineering and Physical Sciences Research Council (EP/J002062/1)