Generatrices of rational curves

Abstract

We investigate the one-parametric set \( \mathbb{G} \) of projective subspaces that is generated by a set of rational curves in projective relation. The main theorem connects the algebraic degree \( \delta \) of \( \mathbb{G} \), the number of degenerate subspaces in \( \mathbb{G} \) and the dimension of the variety of all rational curves that can be used to generate \( \mathbb{G} \). It generalizes classical results and is related to recent investigations on projective motions with trajectories in proper subspaces of the fixed space.