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On threefolds covered by lines

  • Emilia Mezzetti
  • Dario Portelli
Article

Abstract

A classification theorem is given of projective threefolds that are covered by the lines of a two-dimensional family, but not by a higher dimensional family. Precisely, ifX is such a threefold, let Σ denote the Fano scheme of lines onX and μ the number of lines contained inX and passing through a general point ofX. Assume that Σ is generically reduced. Then μ ≤ 6. Moreover,X is birationally a scroll over a surface (μ = 1), orX is a quadric bundle, orX belongs to a finite list of threefolds of degree at most 6. The smooth varieties of the third type are precisely the Fano threefolds with −K X = 2H X .

Keywords

General Point Irreducible Component General Line Singular Locus Hyperplane Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Mathematische Seminar 2000

Authors and Affiliations

  1. 1.Dipartimento di Scienze MatematicheUniversità degli Studi di TriesteTriesteItalia

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