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.
Titolo: | Non-reductive automorphism groups, the Loewy filtration and K-stability |
Autori: | |
Data di pubblicazione: | 2016 |
Rivista: | |
Citazione: | Codogni, G., & Dervan, R. (2016). Non-reductive automorphism groups, the Loewy filtration and K-stability. ANNALES DE L'INSTITUT FOURIER, 66(5), 1895-1921. |
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. |
Handle: | http://hdl.handle.net/11590/302593 |
Appare nelle tipologie: | 1.1 Articolo in rivista |