Frobenius integrability of certain $p$-forms on singular spaces

Junyan Cao; Andreas Höring

doi:10.5802/crmath.582

Article de recherche - Géométrie algébrique

Frobenius integrability of certain

p

-forms on singular spaces
[Intégrabilité au sens de Frobenius pour certaines p-formes sur des espaces singuliers]

Junyan Cao ¹ ; Andreas Höring ¹

¹ Université Côte d’Azur, CNRS, LJAD, France, Institut universitaire de France

Comptes Rendus. Mathématique, Volume 362 (2024) no. S1, pp. 43-54.

Résumé
Abstract

Demailly a montré que la distribution définie par une p-forme holomorphe à valeurs dans un fibré en droites est toujours intégrable si la variété est kählerienne compacte et le dual du fibré en droites est pseudoeffectif. Nous généralisons son résultat à des espaces kähleriennes compactes à singularités klt.

Demailly proved that on a smooth compact Kähler manifold the distribution defined by a holomorphic $p$ -form with values in an anti-pseudoeffective line bundle is always integrable. We generalise his result to compact Kähler spaces with klt singularities.

Reçu le : 2022-12-12
Accepté le : 2023-06-19
Publié le : 2024-06-06

DOI : 10.5802/crmath.582

Classification : 14E30, 32Q15, 32J25
Keywords: holomorphic $p$-forms, klt spaces, foliations
Mot clés : $p$-forme holomorphe, espace à singularités klt, feuilletages

Affiliations des auteurs :

Junyan Cao ¹ ; Andreas Höring ¹

¹ Université Côte d’Azur, CNRS, LJAD, France, Institut universitaire de France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Frobenius integrability of certain $p$-forms on singular spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {43--54},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     number = {S1},
     year = {2024},
     doi = {10.5802/crmath.582},
     language = {en},
}

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Junyan Cao; Andreas Höring. Frobenius integrability of certain $p$-forms on singular spaces. Comptes Rendus. Mathématique, Volume 362 (2024) no. S1, pp. 43-54. doi : 10.5802/crmath.582. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.582/

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