Comptes Rendus
no. 2
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

Hélène Esnault1 ; Daqing Wan2
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, Volume 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
Hélène Esnault 1 ; Daqing Wan 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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Hélène Esnault; Daqing Wan. Hodge type of the exotic cohomology of complete intersections. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 153-157. doi : 10.1016/S1631-073X(03)00013-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00013-X/

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[3] P. Deligne; A. Dimca Filtrations de Hodge et par l'ordre du pôle pour les hypersurfaces singulières, Ann. Sci. École Norm. Sup. (4), Volume 23 (1990), pp. 645-656

[4] B. Dwork On the rationality of the zeta function of an algebraic variety, Amer. J. Math., Volume 82 (1960), pp. 631-648

[5] H. Esnault Hodge type of subvarieties of ℙ n of small degrees, Math. Ann., Volume 288 (1990) no. 3, pp. 549-551

[6] H. Esnault; M. Nori; V. Srinivas Hodge type of projective varieties of low degree, Math. Ann., Volume 293 (1992) no. 1, pp. 1-6

[7] N. Katz On a theorem of Ax, Amer. J. Math., Volume 93 (1971), pp. 485-499

[8] D. Wan Poles of zeta functions of complete intersections, Chinese Ann. Math., Volume 21B (2000) no. 2, pp. 187-200

Cité par Sources :

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

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