Claire Voisin

Title: On the coniveau of rationally connected 3-folds

Abstract:
It is known that the integral cohomology of positive degree of a rationally connected projective 
complex manifold has coniveau at least 1, that is, is supported on a proper subvariety. However 
it is unknown whether it comes from the cohomology of a smooth projective variety of smaller 
dimension by a Gysin morphism (that is, whether it is of strong coniveau at least 1, following the 
terminology of Benoist and Ottem). This last property is a necessary condition for stable rationality. 
We prove that it is satisfied by rationally connected threefolds.