On the k-unirationality of the cubic complex

Abstract

We show that the complete intersection V = V(2,3) ⊆ ℙ5 of a quadric and a cubic in 5-dimensional projective space defined over a field k, of char. ≠ 2,3, is unirational over this field k itself if moreover V has a point p rational over k and if one of the two planes through p on the quadric is also rational over k.