Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties
- 1 June 2007
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 59 (3), 488-502
- https://doi.org/10.4153/cjm-2007-021-6
Abstract
We consider the k-osculating varieties Ok,n.d to the (Veronese) d-uple embeddings of ℙn. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes Y ⊂ ℙn to and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.Keywords
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