On the coniveau of rationally connected threefolds

TL;DR

This paper demonstrates that the integral cohomology of rationally connected threefolds is derived from the cohomology of smooth curves, establishing a strong coniveau property in algebraic geometry.

Contribution

It proves that the integral cohomology of rationally connected threefolds is generated by the cohomology of smooth curves through the cylinder homomorphism.

Findings

Integral cohomology modulo torsion is from smooth curves

Cohomology is of strong coniveau 1

Uses cylinder homomorphism associated to 1-cycles

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.