On the weak non-defectivity of veronese embeddings of projective spaces
Edoardo Ballico
Open Mathematics, Tome 3 (2005), p. 183-187 / Harvested from The Polish Digital Mathematics Library
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Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(nn+x). Here we prove that the order x Veronese embedding ofP n is not weakly (k−1)-defective, i.e. for a general S⊃P n such that #(S) = k+1 the projective space | I 2S (x)| of all degree t hypersurfaces ofP n singular at each point of S has dimension (n/n+x )−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I 2S (x)| has an ordinary double point at each P∈ S and Sing (F)=S.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:268907 
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     title = {On the weak non-defectivity of veronese embeddings of projective spaces},
     journal = {Open Mathematics},
     volume = {3},
     year = {2005},
     pages = {183-187},
     zbl = {1106.14040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02479194}
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Edoardo Ballico. On the weak non-defectivity of veronese embeddings of projective spaces. Open Mathematics, Tome 3 (2005) pp. 183-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02479194/

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