Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds

Dervan, R. (2016) Alpha invariants and coercivity of the Mabuchi functional on Fano manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, 25(4), pp. 919-934. (doi: 10.5802/afst.1515)

Abstract

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Dervan, Dr Ruadhaí
• Authors: Dervan, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Annales de la Faculté des sciences de Toulouse : Mathématiques
• Publisher: Institut de Mathématiques de Toulouse
• ISSN: 0240-2963
• ISSN (Online): 2258-7519
• Copyright Holders: Copyright © Université Paul Sabatier, Toulouse, 2016
• First Published: First published in Annales de la Faculté des sciences de Toulouse : Mathématiques 25(4):919-934
• Publisher Policy: Reproduced under a Creative Commons licence