On rational normal curves in projective space

In this article we consider a generalization of a well-known result by Veronese about rational normal curves. More precisely, given a collection of linear spaces in P^n, we study the existence of rational normal curves intersecting each component of the configuration maximally. We introduce different methods to show the existence and non-existence of such curves. We also show how to apply these techniques to the study of defectivity of Segre-Veronese varieties.