Potential density of rational points on the variety of lines of a cubic fourfold

Claire Voisin
Université de Paris VII (Denis Diderot) et Université de Paris VI (Pierre et Marie Curie)

This is joint work with E. Amerik. We show that for many cubic fourfolds defined over a number field K, there is a number field L such that the L-points of the variety of lines F(X) are Zariski dense in F(X). These varieties F(X) have Picard number 1 (for K3 surfaces, there is no example with Picard number 1 known to satisfy the above density property, while it is conjectured to always hold). The proof involves among other things the $l$-adic Abel-Jacobi invariant of a certain cycle and a result of Green-Griffiths-Paranjape.


Back to Workshop in Celebration of Mark Green's 60th Birthday: Hodge Theory and Algebraic Geometry