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Article Dans Une Revue Geometry and Topology Année : 2021

On the coniveau of rationally connected threefolds

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 N n−2 H 2n−3 (X, Z) and coniveau N n−2 H 2n−3 (X, Z) coincide for cohomology modulo torsion.
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hal-03403497 , version 1 (26-10-2021)

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  • HAL Id : hal-03403497 , version 1

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Claire Voisin. On the coniveau of rationally connected threefolds. Geometry and Topology, In press. ⟨hal-03403497⟩
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