On the structure of ideal class groups of CM-fields.
Kurihara, Masato (2003)
Documenta Mathematica
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Kurihara, Masato (2003)
Documenta Mathematica
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Haggard, Paul W., Kiltinen, John O. (1980)
International Journal of Mathematics and Mathematical Sciences
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Štefan Schwarz (1950)
Časopis pro pěstování matematiky a fysiky
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Bley, W. (2006)
Documenta Mathematica
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Abbas, Yousef, Liang, Joseph J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Jitka Kühnová (1979)
Archivum Mathematicum
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Robbins, Neville (1988)
International Journal of Mathematics and Mathematical Sciences
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Sury, B. (2009)
Journal of Integer Sequences [electronic only]
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Edoardo Ballico (2005)
Open Mathematics
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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.