Classes de Hirzebruch et classes de Chern motiviques

Jean-Paul Brasselet; Jörg Schürmann; Shoji Yokura

doi:10.1016/j.crma.2005.12.022

Géométrie algébrique

Classes de Hirzebruch et classes de Chern motiviques
[Hirzebruch classes and motivic Chern classes]

Presented by: Bernard Malgrange

Jean-Paul Brasselet ¹; Jörg Schürmann ²; Shoji Yokura ³

¹ IML, case 907, Luminy, 13288 Marseille cedex 9, France
² Westf. Wilhelms-Universität, SFB 478 “Geometrische Strukturen in der Mathematik”, Hittorfstr. 27, 48149 Münster, Allemagne
³ Department of Mathematics and Computer Science, Faculty of Science, University of Kagoshima, 21-35 Korimoto 1-chome, Kagoshima 890-0065, Japon

Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 325-328.

Abstract
Résumé

Let X be a complex algebraic variety. We define and study new theories of characteristic classes, defined on the relative Grothendieck group of complex algebraic varieties over X as introduced and studied by Looijenga and Bittner in relation to motivic integration. One of them, $T_{y}$ is a homology class version of the motivic measure and generalizes the corresponding Hirzebruch characteristic. It unifies the Chern class transformation of Schwartz and MacPherson, the Todd class transformation of Baum–Fulton–MacPherson and the L-class transformation of Cappell–Shaneson.

Étant donnée une variété algébrique complexe X, nous introduisons de nouvelles théories de classes caractéristiques, définies sur le groupe de Grothendieck relatif des variétés algébriques complexes sur X, construit et étudié par Looijenga et Bittner dans le cadre de l'intégration motivique. L'une d'entre elles $T_{y}$ est une version homologique de la mesure motivique et généralise la caractéristique d'Hirzebruch correspondante. Elle unifie la transformation de Chern de Schwartz–MacPherson, la transformation de Todd de Baum–Fulton–MacPherson et la transformation de L-classe de Cappell–Shaneson.

Received: 2004-09-30
Accepted: 2005-12-21
Published online: 2006-01-18

DOI: 10.1016/j.crma.2005.12.022

Author's affiliations:

Jean-Paul Brasselet ¹; Jörg Schürmann ²; Shoji Yokura ³

¹ IML, case 907, Luminy, 13288 Marseille cedex 9, France
² Westf. Wilhelms-Universität, SFB 478 “Geometrische Strukturen in der Mathematik”, Hittorfstr. 27, 48149 Münster, Allemagne
³ Department of Mathematics and Computer Science, Faculty of Science, University of Kagoshima, 21-35 Korimoto 1-chome, Kagoshima 890-0065, Japon

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     author = {Jean-Paul Brasselet and J\"org Sch\"urmann and Shoji Yokura},
     title = {Classes de {Hirzebruch} et classes de {Chern} motiviques},
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Jean-Paul Brasselet; Jörg Schürmann; Shoji Yokura. Classes de Hirzebruch et classes de Chern motiviques. Comptes Rendus. Mathématique, Volume 342 (2006) no. 5, pp. 325-328. doi : 10.1016/j.crma.2005.12.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.022/

References
Cited by

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