We give a factorization of the cycle of a bounded complex of vector bundles in terms of certain associated differential forms and residue currents. This is a generalization of previous results in the case when the complex is a locally free resolution of the structure sheaf of an analytic space and it can be seen as a generalization of the classical Lelong–Poincaré formula.
Nous donnons une factorisation du cycle associé à un complexe de fibrés vectoriels comme produit d’un certain courant résiduel (construit à l’aide de ce complexe) et d’une forme différentielle lisse. C’est une généralisation de résultats antérieurs où le complexe est une résolution localement libre du faisceau structural d’un espace analytique. Ce résultat peut être interprété comme une version abstraite de la formule de Lelong–Poincaré.
Accepted:
Published online:
Richard Lärkäng 1; Elizabeth Wulcan 1
CC-BY 4.0
@article{AFST_2021_6_30_5_961_0,
author = {Richard L\"ark\"ang and Elizabeth Wulcan},
title = {Residue currents and cycles of complexes of vector bundles},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {961--984},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 30},
number = {5},
year = {2021},
doi = {10.5802/afst.1692},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1692/}
}
TY - JOUR AU - Richard Lärkäng AU - Elizabeth Wulcan TI - Residue currents and cycles of complexes of vector bundles JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2021 SP - 961 EP - 984 VL - 30 IS - 5 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1692/ DO - 10.5802/afst.1692 LA - en ID - AFST_2021_6_30_5_961_0 ER -
%0 Journal Article %A Richard Lärkäng %A Elizabeth Wulcan %T Residue currents and cycles of complexes of vector bundles %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2021 %P 961-984 %V 30 %N 5 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1692/ %R 10.5802/afst.1692 %G en %F AFST_2021_6_30_5_961_0
Richard Lärkäng; Elizabeth Wulcan. Residue currents and cycles of complexes of vector bundles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 5, pp. 961-984. doi : 10.5802/afst.1692. https://afst.centre-mersenne.org/articles/10.5802/afst.1692/
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