We consider the k-osculating varietiesOk,d to the Veronese d?uple embeddings of P2. By studying the Hilbert function of certain zero-dimensional schemes Y ⊂ P2, we find the dimension of Os k,d, the (s?1)th secant varieties of Ok,d, for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.
@article{urn:eudml:doc:41810,
title = {Some defective secant varieties to osculating varieties of Veronese surfaces.},
journal = {Collectanea Mathematica},
volume = {57},
year = {2006},
pages = {43-68},
zbl = {1105.14053},
mrnumber = {MR2206180},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41810}
}
Bernardi, Alessandra; Catalisano, Maria Virginia. Some defective secant varieties to osculating varieties of Veronese surfaces.. Collectanea Mathematica, Tome 57 (2006) pp. 43-68. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41810/