On the weak non-defectivity of veronese embeddings of projective spaces |
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Authors: | Ballico Edoardo |
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Affiliation: | (1) Department of Mathematics, University of Trento, 38050 Povo (TN), Italy |
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Abstract: | Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<( n n+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. The author was partially supported by MIUR and GNSAGA of INdAM (Italy). |
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Keywords: | Veronese variety weakly defective variety zero-dimensional scheme double point fat point Veronese embedding |
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