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Stability of equivariant logarithmic tangent sheaves on toric varieties of Picard rank two
Achim Napame1
1 Université 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
Mot 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 
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     title = {Stability of equivariant logarithmic tangent sheaves on toric varieties of {Picard} rank two},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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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. https://afst.centre-mersenne.org/articles/10.5802/afst.1786/

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