Non-reductive automorphism groups, the Loewy filtration and K-stability

Codogni, G. and Dervan, R. (2016) Non-reductive automorphism groups, the Loewy filtration and K-stability. Annales de l’institut Fourier, 66(5), pp. 1895-1921. (doi: 10.5802/aif.3052)

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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 examples which we compute. We conjecture this holds in general. This is an algebro-geometric analogue of Matsushima’s theorem regarding the existence of constant scalar curvature Kähler metrics. As an application, we give an example of an orbifold del Pezzo surface without a Kähler-Einstein metric.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Dervan, Dr Ruadhaí
Authors: Codogni, G., and Dervan, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Annales de l’institut Fourier
Publisher:Association des Annales de l'Institut Fourier
ISSN (Online):1777-5310
Copyright Holders:Copyright © Association des Annales de l’institut Fourier, 2016
First Published:First published in Annales de l'Institut Fourier 66(5):1895-1921
Publisher Policy:Reproduced under a Creative Commons licence

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