SMF

A few remarks on the lifting problem

A few remarks on the lifting problem

L. CHIANTINI, C. CILIBERTO
     
                
  • Année : 1993
  • Tome : 218
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 14E25
  • Pages : 95-109
  • DOI : 10.24033/ast.241

We start with a projective variety X in Pr and a family W of projective subvarieties of Pr, parametrized by the space B, such that for any t B the corresponding fibre Wt of W is contained in some h-plane Lt, and Wt X Lt ; we assume that the Lt's for variable t fill an open dense subset of the corresponding Grassmannian. We give conditions on the degrees of X and Wt which imply that the varieties Wt glue together to give a variety W (containing X ) such that Wt = W Lt for all t. The proofs are based on the ical differential theory of “foci” introduced by C. Segre. Our results generaIize the theorems of Laudal and Gruson-Peskine, which deal with the case X is a curve in P3



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