On the weak non-defectivity of veronese embeddings of projective spaces
Open Mathematics (2005)
- Volume: 3, Issue: 2, page 183-187
- ISSN: 2391-5455
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topEdoardo Ballico. "On the weak non-defectivity of veronese embeddings of projective spaces." Open Mathematics 3.2 (2005): 183-187. <http://eudml.org/doc/268907>.
@article{EdoardoBallico2005,
abstract = {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.},
author = {Edoardo Ballico},
journal = {Open Mathematics},
keywords = {14N05},
language = {eng},
number = {2},
pages = {183-187},
title = {On the weak non-defectivity of veronese embeddings of projective spaces},
url = {http://eudml.org/doc/268907},
volume = {3},
year = {2005},
}
TY - JOUR
AU - Edoardo Ballico
TI - On the weak non-defectivity of veronese embeddings of projective spaces
JO - Open Mathematics
PY - 2005
VL - 3
IS - 2
SP - 183
EP - 187
AB - 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.
LA - eng
KW - 14N05
UR - http://eudml.org/doc/268907
ER -
References
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- [8] C. Ciliberto: “Geometric aspects of polynomial interpolation in more variables and of Waring's problem”, In European Congress of Mathematics (Barcelona, 2000), Progress in Math., Vol. 201, Birkhäuser, Basel 2001, pp. 289–316. Zbl1078.14534
- [9] C. Ciliberto and A. Hirschowitz: “Hypercubique de ℙ4 avec sept points singulieres génériques”, C. R. Acad. Sci. Paris, Vol. 313(1), (1991), pp. 135–137.
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