Curves on threefolds and a conjecture of Griffiths-Harris
arXiv:1005.3982 · doi:10.1007/s00208-009-0376-y
Abstract
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.
14 pages