From the coordinates of lines to ruled varieties (Q1861450)

This is a very well-written survey paper on ruled varieties. The author starts with a short survey of Plücker construction of line coordinates and the concept of duality in projective geometry. This allows him to define in three-dimensional projective space skew ruled surfaces (quadrics, cones, tangential varieties) and developable surfaces. In the second part of the paper, the author introduces the Grassmannians and uses them to define the generalization of ruled varieties to higher dimensions. In particular, he presents here the Hartman-Nirenberg cylinder theorem and the construction and classification of developable varieties (the varieties with degenerate Gauss maps) of Gauss rank one. In conclusion, the author considers some results on developable varieties of rank higher than one.