We introduce the notion of ”sub–defective’ varieties as those varieties X forwhich a general tangent space intersects ”too many” other tangent spaces to X. Weshow that this notion has an unexpected link with the study of varieties with degenerateosculating behavior. Namely we show that sub-defective surfaces are precisely thosesurfaces whose general osculating space is bi-osculating.
Triple points imposing triple divisors and the defective hierarchy / C. Bocci, L. Chiantini - In: Projective varieties with unexpected properties / C. Ciliberto, A. V. Geramita, B. Harbourne, R. M. Miró-Roig, K. Ranestad. - [s.l] : Walter de Gruyter GmbH & Co. KG, 2005. - ISBN 978-3-11-018160-9. - pp. 33-49
Triple points imposing triple divisors and the defective hierarchy
C. BocciPrimo
;
2005
Abstract
We introduce the notion of ”sub–defective’ varieties as those varieties X forwhich a general tangent space intersects ”too many” other tangent spaces to X. Weshow that this notion has an unexpected link with the study of varieties with degenerateosculating behavior. Namely we show that sub-defective surfaces are precisely thosesurfaces whose general osculating space is bi-osculating.
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