We consider the k-osculating varieties O(k,d) to the Veronese d-uple embeddings of P2. By studying the Hilbert function of certain zero-dimensional schemes Y subset of P2, we find the dimension of O^s(k,d), the (s - 1)-th secant varieties of O(k,d), for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.
Some defective secant varieties to osculating varieties of Veronese surfaces
CATALISANO, MARIA VIRGINIA
2006-01-01
Abstract
We consider the k-osculating varieties O(k,d) to the Veronese d-uple embeddings of P2. By studying the Hilbert function of certain zero-dimensional schemes Y subset of P2, we find the dimension of O^s(k,d), the (s - 1)-th secant varieties of O(k,d), for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.File in questo prodotto:
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