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Pré-Publication, Document De Travail Année : 2001

Severi varieties

P. E. Chaput

Résumé

R. Hartshorne conjectured and F. Zak proved that any n-dimensional smooth non-degenerate complex algebraic variety X in a m-dimensional projective space P satisfies Sec(X)=P if m<3n/2+2. In this article, I deal with the limiting case of this theorem, namely the Severi varieties, defined by the conditions m=3n/2+2 and Sec(X) different from P. I want to give a different proof of a theorem of F. Zak classifying all Severi varieties: I will prove that any Severi variety is homogeneous and then deduce their classification and the following geometric property : the derivatives of the equation of Sec(X), which is a cubic hypersurface, determine a birational morphism of P.

Dates et versions

hal-00136978 , version 1 (16-03-2007)

Identifiants

Citer

P. E. Chaput. Severi varieties. 2001. ⟨hal-00136978⟩

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