On the coniveau of rationally connected threefolds

Voisin, Claire¹

¹ Institut de mathématiques de Jussieu, CNRS, Paris, France

Geometry & topology, Tome 26 (2022) no. 6, pp. 2731-2772.

Résumé

We prove that the integral cohomology modulo torsion of a rationally connected threefold comes from the integral cohomology of a smooth curve via the cylinder homomorphism associated to a family of $1$–cycles. Equivalently, it is of strong coniveau $1$. More generally, for a rationally connected manifold $X$ of dimension $n$, we show that the strong coniveau ${Ñ}^{n-2}{H}^{2n-3}(X,\mathbb{Z})$ and coniveau $N^{n-2}{H}^{2n-3}(X,\mathbb{Z})$ coincide for cohomology modulo torsion.

Détail

Keywords: Cohomology, coniveau, birational invariants, rationally connected manifolds

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