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.

Codogni, G., & Dervan, R. (2016). Non-reductive automorphism groups, the Loewy filtration and K-stability. ANNALES DE L'INSTITUT FOURIER, 66(5), 1895-1921 [10.5802/aif.3052].

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

CODOGNI, GIULIO;
2016

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.
Codogni, G., & Dervan, R. (2016). Non-reductive automorphism groups, the Loewy filtration and K-stability. ANNALES DE L'INSTITUT FOURIER, 66(5), 1895-1921 [10.5802/aif.3052].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/302593
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