Osculating properties of decomposable scrolls

Osculating spaces of decomposable scrolls (of any genus and not necessarily normal) are studied and their inflectional loci are related to those of their generating curves by using systematically an idea introduced by Piene and Sacchiero in the setting of rational normal scrolls. In this broader setting the extra components of the second discriminant locus -deriving from flexes- are investigated and a new class of uninflected surface scrolls is presented and characterized. Further properties related to osculation are discussed for (not necessarily decomposable) scrolls.