arXiv:1412.1426 Abstract | arXiv Analytics

arXiv:1412.1426 [math.DG]Abstract References Reviews Resources

Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds

Published 2014-12-03Version 1

We give a criterion for the coercivity of the Mabuchi functional for general K\"ahler 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 K\"ahler-Einstein metric. As an application, we provide new K\"ahler classes on a general degree one del Pezzo surface for which the Mabuchi functional is coercive.

Comments: 13 pages, comments welcome

Categories: math.DG, math.CV

Keywords: mabuchi functional, fano manifolds, coercivity, tians alpha invariant, del pezzo surface

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