Curves on threefolds and a conjecture of Griffiths-Harris

Details Curves on threefolds and a conjecture of Griffiths-Harris Curves on threefolds and a conjecture of Griffiths-Harris

2010-05-21

arxiv.org/abs/1005.3982v1

Mathematische Annalen Volume 345, Number 3 / November 2009, 731-748

Mathematics

Algebraic Geometry

14 pages

Scientific paper

10.1007/s00208-009-0376-y

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

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