Algebraic Geometry
Hodge type of the exotic cohomology of complete intersections
[Type de Hodge de la cohomologie exotique des intersections complètes]

Présenté par : Pierre Deligne

Esnault, Hélène1 ; Wan, Daqing2
1 Mathematik, Universität Essen, FB 6, Mathematik, 45117 Essen, Germany
2 Department of Mathematics, University of California, Irvine, CA 92697-3875, USA
Comptes Rendus. Mathématique, Tome 336 (2003) no. 2, pp. 153-157.

Si X⊂ℙ n est une intersection complète lisse, sa cohomologie modulo celle de ℙ n est supportée en dimension moitié. Si l'intersection complète est singulière, elle peut aussi avoir de la cohomologie exotique en dimension supérieure. Nous montrons qu' on peut améliorer le type de Hodge de cette cohomologie de de Rham exotique.

If X⊂ℙ n is a smooth complete intersection, its cohomology modulo the one of ℙ n is supported in middle dimension. If the complete intersection is singular, it might also carry exotic cohomology beyond the middle dimension. We show that for this exotic cohomology, one can improve the known bound for the Hodge type of its de Rham cohomology.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00013-X
Esnault, Hélène 1 ; Wan, Daqing 2

1 Mathematik, Universität Essen, FB 6, Mathematik, 45117 Essen, Germany
2 Department of Mathematics, University of California, Irvine, CA 92697-3875, USA 
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Esnault, Hélène; Wan, Daqing. Hodge type of the exotic cohomology of complete intersections. Comptes Rendus. Mathématique, Tome 336 (2003) no. 2, pp. 153-157. doi : 10.1016/S1631-073X(03)00013-X. http://www.numdam.org/articles/10.1016/S1631-073X(03)00013-X/

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☆ The first author is supported by the DFG-Schwerpunkt “Komplexe Mannigfaltigkeiten” while the second author is partially supported by the NSF.