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

Voisin, C *(Jussieu)*

Thursday 28 April 2011, 14:00-15:00

Seminar Room 1, Newton Institute

#### 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 $Y$.