On the coniveau of rationally connected threefolds

Abstract

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 in the sense of Benoist-Ottem.

arXiv commentFinal version to appear in Geometry and Topology

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Cited by in corpus (2)

• Factorization of the Abel-Jacobi maps
• Cylinder maps of algebraic cycles on cubic hypersurfaces