On the dual variety in characteristic 2
Edoardo Ballico (1990)
Compositio Mathematica
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Edoardo Ballico (1990)
Compositio Mathematica
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Joe Harris (1981)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.
Gao, Peng (2001)
International Journal of Mathematics and Mathematical Sciences
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Laura Costa, Rosa Miró-Roig (2012)
Open Mathematics
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This paper aims to construct a full strongly exceptional collection of line bundles in the derived category D b(X), where X is the blow up of ℙn−r ×ℙr along a multilinear subspace ℙn−r−1×ℙr−1 of codimension 2 of ℙn−r ×ℙr. As a main tool we use the splitting of the Frobenius direct image of line bundles on toric varieties.
Anwar, Matloob, Pecaric, Josip E. (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Adil Khan, M., Pečarić, J.E. (2010)
Journal of Inequalities and Applications [electronic only]
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Keel, Seán (1999)
Annals of Mathematics. Second Series
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Michael Burr (2012)
Open Mathematics
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For a complex irreducible projective variety, the volume function and the higher asymptotic cohomological functions have proven to be useful in understanding the positivity of divisors as well as other geometric properties of the variety. In this paper, we study the vanishing properties of these functions on hypersurfaces of ℙn × ℙn. In particular, we show that very general hypersurfaces of bidegree (k, k) obey a very strong vanishing property, which we define as asymptotic purity: at...
Böhning, Christian (2006)
Documenta Mathematica
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Zudilin, Wadim (2005)
Séminaire Lotharingien de Combinatoire [electronic only]
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