We consider the k-osculating varieties O(k,n,d) to the (Veronese) d-uple embeddings of P^n. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes of P-n to O^s(k,n,d) and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.

Osculating Varieties of Veronese Varieties and Their Higher Secant Varieties

CATALISANO, MARIA VIRGINIA;
2007-01-01

Abstract

We consider the k-osculating varieties O(k,n,d) to the (Veronese) d-uple embeddings of P^n. We study the dimension of their higher secant varieties via inverse systems (apolarity). By associating certain 0-dimensional schemes of P-n to O^s(k,n,d) and by studying their Hilbert functions, we are able, in several cases, to determine whether those secant varieties are defective or not.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/222688
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