Comptes Rendus
Géométrie algébrique
Simplicity of tangent bundles of smooth horospherical varieties of Picard number one
Jaehyun Hong1
1 Center for Complex Geometry, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 285-290.

Récemment, Kanemitsu a découvert un contre-exemple à la conjecture de longue date selon laquelle le faisceau tangent d’une variété de Fano de nombre de Picard un est (semi) stable. Son contre-exemple est une variété horosphérique lisse. Une conjecture plus faible affirme que le fibré tangent d’une variété de Fano de nombre de Picard un est simple.

Nous prouvons que cette conjecture plus faible est valable pour les variétés horosphériques lisses de nombre de Picard un. Notre preuve découle de l’existence d’une famille irréductible de courbes rationnelles non pliables dont les vecteurs tangents engendrent les espaces tangents de la variété horosphérique en des points généraux.

Recently, Kanemitsu has discovered a counterexample to the long-standing conjecture that the tangent bundle of a Fano manifold of Picard number one is (semi)stable. His counterexample is a smooth horospherical variety. There is a weaker conjecture that the tangent bundle of a Fano manifold of Picard number one is simple.

We prove that this weaker conjecture is valid for smooth horospherical varieties of Picard number one. Our proof follows from the existence of an irreducible family of unbendable rational curves whose tangent vectors span the tangent spaces of the horospherical variety at general points.

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DOI : 10.5802/crmath.299
Jaehyun Hong 1

1 Center for Complex Geometry, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Jaehyun Hong. Simplicity of tangent bundles of smooth horospherical varieties of Picard number one. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 285-290. doi : 10.5802/crmath.299. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.299/

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