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arXiv · 1501.03372

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

Giulio Codogni·Ruadhaí Dervan
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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 K\"ahler metrics. As an application, we give an example of an orbifold del Pezzo surface without a K\"ahler-Einstein metric.

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Giulio Codogni, Ruadhaí Dervan. 2015-01-14. Non-reductive automorphism groups, the Loewy filtration and K-stability. https://arxiv.org/abs/1501.03372

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