Revista Matemática Iberoamericana


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Volume 29, Issue 4, 2013, pp. 1191–1210
DOI: 10.4171/RMI/753

Published online: 2013-12-15

On varieties with higher osculating defect

Pietro De Poi[1], Roberta Di Gennaro[2] and Giovanna Ilardi[3]

(1) Università di Udine, Italy
(2) Università degli Studi di Napoli “Federico II”, Italy
(3) Università degli Studi di Napoli “Federico II”, Italy

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.

Keywords: Algebraic varieties, osculating defects, higher fundamental forms, Laplace equations, scrolls

De Poi Pietro, Di Gennaro Roberta, Ilardi Giovanna: On varieties with higher osculating defect. Rev. Mat. Iberoam. 29 (2013), 1191-1210. doi: 10.4171/RMI/753