A pullback operation on a class of currents
[Un tiré en arrière sur une classe de courants]
Samuelsson Kalm, Håkan1
1 Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Göteborg (Sweden)
Annales de l'Institut Fourier, Online first, 43 p.

Pour toute application holomorphe f:X→Y entre une variété complexe X et une variété hermitienne complexe Y nous étendons le tiré en arrière f * des formes lisses à une classe de courants. Nous fournissons un calcul de base pour ce tiré en arrière et montrons sous des hypothéses assez faibles qu’il est cohomologiquement correct. La classe de courants que nous considérons contient en particulier le courant de Lelong de tout cycle analytique. Notre tiré en arrière dépend en général de la structure hermitienne de Y mais coïncide avec le tiré en arrière habituel des courants a cas où f est une submersion. La construction est basée sur le morphisme de Gysin dans le géométrie algébrique.

For any holomorphic mapping f:X→Y between a complex manifold X and a complex Hermitian manifold Y we extend the pullback f * from smooth forms to a class of currents. We provide a basic calculus for this pullback and show under quite mild assumptions that it is cohomologically sound. The class of currents we consider contains in particular the Lelong current of any analytic cycle. Our pullback depends in general on the Hermitian structure of Y but coincides with the usual pullback of currents in case f is a submersion. The construction is based on the Gysin mapping in algebraic geometry.

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DOI : 10.5802/aif.3628
Classification : 32U40, 14C17, 32H02, 32C30, 32A27
Keywords: Pullback, current, holomorphic mapping.
Mot clés : Tiré en arrière, courant, application holomorphe.
Samuelsson Kalm, Håkan 1

1 Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Göteborg (Sweden) 
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Samuelsson Kalm, Håkan. A pullback operation on a class of currents. Annales de l'Institut Fourier, Online first, 43 p.

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