Examples on Loewy filtrations and K-stability of Fano varieties with non-reductive automorphism groups

Ito, Atsushi

Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 515-537.

Il est connu que le groupe d’automorphismes d’une variété de Fano K-polystable est réductif. Codogni et Dervan ont construit une filtration canonique de l’anneau des sections, appelée filtration de Loewy, et ont conjecturé que la filtration déstabilise n’importe quelle variété de Fano avec le groupe d’automorphismes non réductif. Dans cette note, nous fournissons un contre-exemple à leur conjecture.

It is known that the automorphism group of a K-polystable Fano manifold is reductive. Codogni and Dervan constructed a canonical filtration of the section ring, called Loewy filtration, and conjectured that the filtration destabilizes any Fano variety with non-reductive automorphism group. In this note, we give a counterexample to their conjecture.

Classification : 14J45, 14L30, 32Q26
Keywords: Loewy filtration, K-stability
Mot clés : filtrations de Loewy, K-stabilité

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