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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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: 0373-0956
• 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