Severi varieties

dc.creatorChaput, P. E.
dc.date2001-02-06
dc.date2001-02-07
dc.date.accessioned2026-07-07T04:40:00Z
dc.date.available2026-07-07T04:40:00Z
dc.descriptionR. 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.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0102042
dc.identifierhttp://arxiv.org/abs/math/0102042
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60897
dc.subjectAlgebraic Geometry
dc.subject14M07; 14M17; 14E07
dc.titleSeveri varieties
dc.typetext

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