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Stability of equivariant logarithmic tangent sheaves on toric varieties of Picard rank two
Achim Napame1
1Université de Bretagne Occidentale, Laboratoire de Mathématiques de Bretagne Atlantique, UMR CNRS 6205, 6 Avenue Victor Le Gorgeu, 29238 Brest
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 3, pp. 739-783

For an equivariant log pair (X,D) where X is a normal toric variety and D a reduced Weil divisor, we study slope-stability of the logarithmic tangent sheaf 𝒯 X (-logD). We give a complete description of divisors D and polarizations L such that 𝒯 X (-logD) is (semi)stable with respect to L when X has a Picard rank one or two.

Pour une paire logarithmique équivariante (X,D) où X est une variété torique normale et D un diviseur de Weil réduit, nous étudions la stabilité au sens de la pente du faisceau tangent logarithmique 𝒯 X (-logD). Nous donnons une description complète des diviseurs réduits D et polarisations L sur X tels que le faisceau tangent logarithmique 𝒯 X (-logD) est (semi)stable par rapport à L lorsque X est une variété torique lisse de rang de Picard un ou deux.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1786
Classification: 14M25
Keywords: Toric varieties, logarithmic tangent sheaves, slope-stability
Mots-clés : Variétés toriques, faisceaux tangent logarithmiques, stabilité au sens de la pente

Achim Napame  1

1 Université de Bretagne Occidentale, Laboratoire de Mathématiques de Bretagne Atlantique, UMR CNRS 6205, 6 Avenue Victor Le Gorgeu, 29238 Brest
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Achim Napame. Stability of equivariant logarithmic tangent sheaves on toric varieties of Picard rank two. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 3, pp. 739-783. doi: 10.5802/afst.1786
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