Ruled surface

Summary

In algebraic geometry, a ruled surface is a smooth projective algebraic surface that maps onto a curve with every fibre a projective line. So it is a family of lines parametrized by a curve, the algebraic analogue of a surface swept out by a moving line. Ruled surfaces, together with the projective plane, are the minimal surfaces of Kodaira dimension $-\infty$. They play a basic role in the classification of surfaces.