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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 Ñn2H2n3(X, ) and coniveau Nn2H2n3(X, ) 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