Comptes Rendus
no. 9
Algebraic geometry
The motive of the Fano surface of lines
[Le motif de la surface des droites]

Présenté par : Claire Voisin

Humberto Diaz1
1 Department of Mathematics, Duke University, Durham, NC, USA
Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 925-930.

Dans cette note, nous prouvons que le motif de Chow de la surface des droites d'une hypersurface cubique lisse dans P4 est de dimension finie dans le sens de Kimura. Ceci constitue un exemple d'une variété qui n'est pas domineé par un produit de courbes, mais dont le motif de Chow est de type abélien.

In this short note, we prove that the Chow motive of the Fano surface of lines on the smooth cubic threefold is finite-dimensional in the sense of Kimura. This gives an example of a variety not dominated by a product of curves whose Chow motive is of Abelian type.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.07.003

Humberto Diaz 1

1 Department of Mathematics, Duke University, Durham, NC, USA 
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Humberto Diaz. The motive of the Fano surface of lines. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 925-930. doi : 10.1016/j.crma.2016.07.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.07.003/

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  • Bruno Kahn Albanese kernels and Griffiths groups, Tunisian Journal of Mathematics, Volume 3 (2021) no. 3, p. 589 | DOI:10.2140/tunis.2021.3.589
  • Robert Laterveer Zero-cycles on self-products of surfaces: some new examples verifying Voisin’s conjecture, Rendiconti del Circolo Matematico di Palermo Series 2, Volume 68 (2019) no. 2, p. 419 | DOI:10.1007/s12215-018-0367-5

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