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2009•NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)Requires access

Curves on threefolds and a conjecture of Griffiths-Harris

G. V. Ravindra

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Abstract

Abstract. We prove that any arithmetically Gorenstein curve on a smooth, general hyper-surface X ⊂ P4 of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in P4. We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group. 1.

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Abstract. We prove that any arithmetically Gorenstein curve on a smooth, general hyper-surface X ⊂ P4 of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in P4. We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group. 1.

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Available abstract

Abstract. We prove that any arithmetically Gorenstein curve on a smooth, general hyper-surface X ⊂ P4 of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in P4. We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group. 1.

Key concepts: Mathematics, Conjecture, Pure mathematics

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