# Abel-Jacobi map, integral Hodge classes and decomposition of the diagonal

Presented by:
C Voisin [Jussieu]
Date:
Thursday 28th April 2011 - 14:00 to 15:00
Venue:
INI Seminar Room 1
Abstract:
Given a smooth projective $3$-fold $Y$, with $H^{3,0}(Y)=0$, the Abel-Jacobi map induces a morphism from each smooth variety parameterizing $1$-cycles in $Y$ to the intermediate Jacobian $J(Y)$. We consider in this talk the existence of families of $1$-cycles in $Y$ for which this induced morphism is surjective with rationally connected general fiber, and various applications of this property. When $Y$ itself is uniruled, we relate this property to the existence of an integral homological decomposition of the diagonal of $Y$.