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Mathematische Annalen

, Volume 345, Issue 3, pp 731–748 | Cite as

Curves on threefolds and a conjecture of Griffiths–Harris

  • G. V. RavindraEmail author
Article

Abstract

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface \({X \subset \mathbb P^{4}}\) of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in \({\mathbb P^4}\). We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.

Mathematics Subject Classification (2000)

14C25 14C30 14F05 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Mathematics and Computer ScienceUniversity of MissouriSt. LouisUSA

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