On varieties with higher osculating defect

Abstract

In this paper, using the method of moving frames, we generalise some of Terracini's results on varieties with tangent defect. In particular, we characterise varieties with higher order osculating defect in terms of Jacobians of higher fundamental forms and moreover we characterise varieties with "small" higher fundamental forms as contained in scrolls.

AMS-LaTeX; 17 pages. To appear in Revista Matemática Iberoaméricana

References in corpus (1)

• Singular hypersurfaces characterizing the Lefschetz properties

Cited by in corpus (1)

• On the hypersurfaces contained in their Hessian