We show that the complete intersection V = V (2, 3) of a quadric and a cubic in 5-dimensional projective space defined over a field k, of char. different from 2 and 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.
On the k-Unirationality of the Cubic Complex
CONTE, Alberto;MARCHISIO, Marina;
2007-01-01
Abstract
We show that the complete intersection V = V (2, 3) of a quadric and a cubic in 5-dimensional projective space defined over a field k, of char. different from 2 and 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.
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