Geodesic
Rationality, universal generation and the integral Hodge conjecture
Shen, Mingmin1
1 KdV Institute for Mathematics, University of Amsterdam, Amsterdam, Netherlands
Geometry & topology, Tome 23 (2019) no. 6, pp. 2861-2898.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We use the universal generation of algebraic cycles to relate (stable) rationality to the integral Hodge conjecture. We show that the Chow group of 1–cycles on a cubic hypersurface is universally generated by lines. Applications are mainly in cubic hypersurfaces of low dimensions. For example, we show that if a generic cubic fourfold is stably rational then the Beauville–Bogomolov form on its variety of lines, viewed as an integral Hodge class on the self product of its variety of lines, is algebraic. In dimensions 3 and 5, we relate stable rationality with the geometry of the associated intermediate Jacobian.

DOI : 10.2140/gt.2019.23.2861
Classification : 14C25, 14C30, 14E08
Keywords: algebraic cycles, Hodge conjecture, cubic threefold, cubic fourfold

Shen, Mingmin 1

1 KdV Institute for Mathematics, University of Amsterdam, Amsterdam, Netherlands 
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Shen, Mingmin. Rationality, universal generation and the integral Hodge conjecture. Geometry & topology, Tome 23 (2019) no. 6, pp. 2861-2898. doi : 10.2140/gt.2019.23.2861. http://geodesic.mathdoc.fr/articles/10.2140/gt.2019.23.2861/

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