Examples on Loewy filtrations and K-stability of Fano varieties with non-reductive automorphism groups
[Exemples de filtrations de Loewy et K-stabilité des variétés de Fano avec groupes d’automorphismes non réductifs]
Annales de l'Institut Fourier, Online first, 23 p.

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.

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DOI : https://doi.org/10.5802/aif.3395
Classification : 14J45,  14L30,  32Q26
Mots clés : filtrations de Loewy, K-stabilité
@unpublished{AIF_0__0_0_A46_0,
     author = {Ito, Atsushi},
     title = {Examples on Loewy filtrations and K-stability of Fano varieties with non-reductive automorphism groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     year = {2021},
     doi = {10.5802/aif.3395},
     language = {en},
     note = {Online first},
}
Ito, Atsushi. Examples on Loewy filtrations and K-stability of Fano varieties with non-reductive automorphism groups. Annales de l'Institut Fourier, Online first, 23 p.

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