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

Osculating properties of decomposable scrolls