A generalization to varieties of a result about curves

Abstract

In [1] the author proves that by starting from two projectively equivalent curves in two independent spaces, a 2-dimensional ruled variety can be generated by the lines joining corresponding points of the two curves, the order of the variety being the sum of the orders of them. In this note we prove that result can be extended to any pair of projectively equivalent irreducible varieties of same dimension lying in two complementary spaces