Courants kählériens et surfaces compactes

Ahcène Lamari

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 1, page 263-285
  • ISSN: 0373-0956

Abstract

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A compact complex surface is shown to be Kähler if and only if it carries a strictly positive d -closed current (in other words, a Kähler current), thanks to Demailly’s regularization theorem. We prove a Harvey-Lawson type characterization of compact manifolds carrying such a current. Using Hodge symmetry, we then give a unified proof of kählerianity for surfaces with even first Betti number.

How to cite

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Lamari, Ahcène. "Courants kählériens et surfaces compactes." Annales de l'institut Fourier 49.1 (1999): 263-285. <http://eudml.org/doc/75335>.

@article{Lamari1999,
abstract = {Le théorème de régularisation de Demailly ramène l’existence d’une métrique kählérienne sur une surface compacte à celle d’un (1-1)-courant strictement positif $d$-fermé (“courant kählérien”). Après avoir démontré un critère d’existence d’un tel courant, nous utilisons la symétrie de Hodge pour donner une démonstration unifiée du caractère kählérien des surfaces compactes à premier nombre de Betti pair.},
author = {Lamari, Ahcène},
journal = {Annales de l'institut Fourier},
keywords = {strictly positive -closed currents; Kähler currents; regularization; Kähler surfaces; Kähler metrics; compact surfaces},
language = {fre},
number = {1},
pages = {263-285},
publisher = {Association des Annales de l'Institut Fourier},
title = {Courants kählériens et surfaces compactes},
url = {http://eudml.org/doc/75335},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Lamari, Ahcène
TI - Courants kählériens et surfaces compactes
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 1
SP - 263
EP - 285
AB - Le théorème de régularisation de Demailly ramène l’existence d’une métrique kählérienne sur une surface compacte à celle d’un (1-1)-courant strictement positif $d$-fermé (“courant kählérien”). Après avoir démontré un critère d’existence d’un tel courant, nous utilisons la symétrie de Hodge pour donner une démonstration unifiée du caractère kählérien des surfaces compactes à premier nombre de Betti pair.
LA - fre
KW - strictly positive -closed currents; Kähler currents; regularization; Kähler surfaces; Kähler metrics; compact surfaces
UR - http://eudml.org/doc/75335
ER -

References

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