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.
Dans cette note, nous prouvons que le motif de Chow de la surface des droites d'une hypersurface cubique lisse dans 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.
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Humberto Diaz 1
@article{CRMATH_2016__354_9_925_0,
author = {Humberto Diaz},
title = {The motive of the {Fano} surface of lines},
journal = {Comptes Rendus. Math\'ematique},
pages = {925--930},
publisher = {Elsevier},
volume = {354},
number = {9},
year = {2016},
doi = {10.1016/j.crma.2016.07.003},
language = {en},
}
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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