Osculating Varieties of Veronesean and their higher secant varieties
Abstract
We consider the varieties Ok,n.d of the k-osculating spaces to the Veronese varieties, the d-uple embeddings of n; we study the dimension of their higher secant varieties. Via inverse systems (apolarity) and the study of certain spaces of forms we are able, in several cases, to determine whether those secant varieties are defective or not.
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