[Intégrabilité au sens de Frobenius pour certaines p-formes sur des espaces singuliers]
Demailly proved that on a smooth compact Kähler manifold the distribution defined by a holomorphic -form with values in an anti-pseudoeffective line bundle is always integrable. We generalise his result to compact Kähler spaces with klt singularities.
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.
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Keywords: holomorphic $p$-forms, klt spaces, foliations
Mots-clés : $p$-forme holomorphe, espace à singularités klt, feuilletages
Cao, Junyan 1 ; Höring, Andreas 1
CC-BY 4.0
@article{CRMATH_2024__362_S1_43_0,
author = {Cao, Junyan and H\"oring, Andreas},
title = {Frobenius integrability of certain $p$-forms on singular spaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {43--54},
year = {2024},
publisher = {Acad\'emie des sciences, Paris},
volume = {362},
number = {S1},
doi = {10.5802/crmath.582},
language = {en},
url = {https://www.numdam.org/articles/10.5802/crmath.582/}
}
TY - JOUR AU - Cao, Junyan AU - Höring, Andreas TI - Frobenius integrability of certain $p$-forms on singular spaces JO - Comptes Rendus. Mathématique PY - 2024 SP - 43 EP - 54 VL - 362 IS - S1 PB - Académie des sciences, Paris UR - https://www.numdam.org/articles/10.5802/crmath.582/ DO - 10.5802/crmath.582 LA - en ID - CRMATH_2024__362_S1_43_0 ER -
%0 Journal Article %A Cao, Junyan %A Höring, Andreas %T Frobenius integrability of certain $p$-forms on singular spaces %J Comptes Rendus. Mathématique %D 2024 %P 43-54 %V 362 %N S1 %I Académie des sciences, Paris %U https://www.numdam.org/articles/10.5802/crmath.582/ %R 10.5802/crmath.582 %G en %F CRMATH_2024__362_S1_43_0
Cao, Junyan; Höring, Andreas. Frobenius integrability of certain $p$-forms on singular spaces. Comptes Rendus. Mathématique, Complex algebraic geometry, in memory of Jean-Pierre Demailly, Tome 362 (2024), pp. 43-54. doi: 10.5802/crmath.582
[1] Contact singularities, Manuscr. Math., Volume 108 (2002) no. 4, pp. 529-541 | DOI | Zbl | MR
[2] MMP for co-rank one foliations on threefolds, Invent. Math., Volume 225 (2021) no. 2, pp. 603-690 | DOI | MR | Zbl
[3] On the Frobenius integrability of certain holomorphic -forms, Complex geometry (Göttingen, 2000), Springer, 2002, pp. 93-98 | MR | DOI | Zbl
[4] Analytic methods in algebraic geometry, Surveys of Modern Mathematics, 1, International Press; Higher Education Press, 2012, viii+231 pages | MR
[5] Codimension foliations with numerically trivial canonical class on singular spaces, Duke Math. J., Volume 170 (2021) no. 1, pp. 95-203 | DOI | Zbl | MR
[6] An optimal extension theorem for 1-forms and the Lipman-Zariski conjecture, Doc. Math., Volume 19 (2014), pp. 815-830 | Zbl | DOI | MR
[7] Differential forms on log canonical spaces, Publ. Math., Inst. Hautes Étud. Sci. (2011) no. 114, pp. 87-169 | DOI | MR | Numdam | Zbl
[8] Reflexive differential forms on singular spaces. Geometry and cohomology, J. Reine Angew. Math., Volume 697 (2014), pp. 57-89 | DOI | Zbl | MR
[9] Projectively flat klt varieties, J. Éc. Polytech., Math., Volume 8 (2021), pp. 1005-1036 | DOI | Zbl | Numdam | MR
[10] Bogomolov-Sommese vanishing on log canonical pairs, J. Reine Angew. Math., Volume 702 (2015), pp. 109-142 | DOI | Zbl | MR
[11] Algebraic geometry, Graduate Texts in Mathematics, 52, Springer, 1977, xvi+496 pages | MR | DOI
[12] Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, 1998, viii+254 pages (with the collaboration of C. H. Clemens and A. Corti) | MR | DOI
[13] Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities, J. Am. Math. Soc., Volume 34 (2021) no. 2, pp. 315-368 | DOI | MR | Zbl
[14] Singular foliations with trivial canonical class, Invent. Math., Volume 213 (2018) no. 3, pp. 1327-1380 | DOI | MR | Zbl
[15] A short analytic proof of closedness of logarithmic forms, Kodai Math. J., Volume 18 (1995) no. 2, pp. 295-299 | DOI | MR | Zbl
[16] Singular rationally connected surfaces with nonzero pluri-forms, Mich. Math. J., Volume 63 (2014) no. 4, pp. 725-745 | DOI | Zbl | MR
[17] Foliations with vanishing Chern classes, Bull. Braz. Math. Soc. (N.S.), Volume 44 (2013) no. 4, pp. 731-754 | DOI | MR | Zbl
[18] On the structure of codimension 1 foliations with pseudoeffective conormal bundle, Foliation theory in algebraic geometry. Proceedings of the conference, New York, NY, USA, September 3–7, 2013, Springer, 2016, pp. 157-216 | DOI | Zbl | MR
[19] Singular contact varieties (2022) (https://arxiv.org/abs/2212.07930)
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