On the k-normality of projected algebraic varieties |
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Authors: | Alberto Alzati Francesco Russo |
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Institution: | (1) Dipartimento di Matematica "F. Enriques" Università degli Studi di Milano Via C. Saldini 50, 20133 Milano ITALIA E-mail: alzati@mat.unimi.it, IT;(2) Departamento de Matematica, Universidade Federal de Pernambuco, Cidade Universitaria, 50670-901 Recife-PE, BRASIL E-mail: frusso@dmat.ufpe.br, BR |
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Abstract: | 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.
Received: 21 January 2002 |
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Keywords: | : k-normality projection ℕ p conditions |
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