On the coniveau of rationally connected threefolds

Voisin, Claire

doi:10.2140/gt.2022.26.2731

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On the coniveau of rationally connected threefolds

Claire Voisin

Geometry & Topology 26 (2022) 2731–2772

DOI: 10.2140/gt.2022.26.2731

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 $1$ . More generally, for a rationally connected manifold $X$ of dimension $n$ , we show that the strong coniveau $Ñ^{n - 2} H^{2 n - 3} (X, ℤ)$ and coniveau $N^{n - 2} H^{2 n - 3} (X, ℤ)$ coincide for cohomology modulo torsion.

Keywords

Cohomology, coniveau, birational invariants, rationally connected manifolds

Mathematical Subject Classification

Primary: 14C25, 14E08, 14F99, 14J30, 14M22

References

Publication

Received: 1 December 2020

Revised: 27 April 2021

Accepted: 19 June 2021

Published: 13 December 2022

Proposed: Mark Gross

Seconded: Gang Tian, Lothar Göttsche

Authors

Claire Voisin
Institut de mathématiques de Jussieu CNRS Paris France

Volume 26, issue 6 (2022)