Unirationality of certain surfaces

Nonsingular cubic surfaces in P³ and nonsingular intersections of two quadrics in P⁴ are investigated. It is proved that if a k-point exists on a surface, there is a k-point not on a line; k is the field over which the surfaces are defined.Translated from Matematicheskie Zametki, Vol. 5, No. 2, pp. 155–159, February, 1969.The author expresses his gratitude to Yu. I. Manin, under whose direction this work has been written.