On the k-normality of projected algebraic varieties

  • Alberto Alzati
  • Francesco Russo


We give a necessary and sufficient condition for the isomorphic projection of a k-normal variety to remain k-normal, k ≥ 2; the condition is based on a scheme ℤk naturally associated to degree k forms vanishing on the variety. We furnish many applications and examples especially in the case of varieties defined by quadratic equations. A non-vanishing theorem for the Koszul cohomology of projected varieties allows us to construct interesting examples in the last sections. All the results are effective and also interesting from the computational point of view.

Keywords: k-normality, projection, ℕp conditions. 
Mathematical subject classification: Primary 14N05; Secondary 14J40. 


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Copyright information

© Sociedade Brasileira de Matemática 2002

Authors and Affiliations

  • Alberto Alzati
    • 1
  • Francesco Russo
    • 2
  1. 1.Dipartimento di Matematica "F. Enriques" Università degli Studi di Milano Via C. Saldini 50, 20133 Milano ITALIA E-mail: alzati@mat.unimi.itItaly
  2. 2.Departamento de Matematica, Universidade Federal de Pernambuco, Cidade Universitaria, 50670-901 Recife-PE, BRASIL E-mail: frusso@dmat.ufpe.brBrazil

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