In this paper we study the positivity of the cotangent bundle of projective manifolds. We conjecture that the cotangent bundle is pseudoeffective if and only the manifold has non-zero symmetric differentials. We confirm this conjecture for most projective surfaces that are not of general type.
Dans ce papier nous étudions la positivité du fibré cotangent des variétés projective lisses. Nous conjecturons que le fibré cotangent est pseudoeffectif si et seulement si la variété possède des formes holomorphes symétriques non-nulles. Nous montrons cette conjecture pour la plupart des surfaces projectives lisses qui ne sont pas de type général.
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Keywords: MMP, minimal models, positivity of vector bundles, nonvanishing conjecture, symmetric differentials
Höring, Andreas 1 ; Peternell, Thomas 2
CC-BY 4.0
@article{AFST_2023_6_32_5_855_0,
author = {H\"oring, Andreas and Peternell, Thomas},
title = {A {Nonvanishing} {Conjecture} for {Cotangent} {Bundles}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {855--892},
year = {2023},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 32},
number = {5},
doi = {10.5802/afst.1756},
language = {en},
url = {https://www.numdam.org/articles/10.5802/afst.1756/}
}
TY - JOUR AU - Höring, Andreas AU - Peternell, Thomas TI - A Nonvanishing Conjecture for Cotangent Bundles JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2023 SP - 855 EP - 892 VL - 32 IS - 5 PB - Université Paul Sabatier, Toulouse UR - https://www.numdam.org/articles/10.5802/afst.1756/ DO - 10.5802/afst.1756 LA - en ID - AFST_2023_6_32_5_855_0 ER -
%0 Journal Article %A Höring, Andreas %A Peternell, Thomas %T A Nonvanishing Conjecture for Cotangent Bundles %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2023 %P 855-892 %V 32 %N 5 %I Université Paul Sabatier, Toulouse %U https://www.numdam.org/articles/10.5802/afst.1756/ %R 10.5802/afst.1756 %G en %F AFST_2023_6_32_5_855_0
Höring, Andreas; Peternell, Thomas. A Nonvanishing Conjecture for Cotangent Bundles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 5, pp. 855-892. doi: 10.5802/afst.1756
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