Curves on threefolds and a conjecture of Griffiths–Harris

2009/05/27 by G. V. Ravindra · 8 citations
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complete intersection #Conjecture #Degree (music) #Geometry and complex manifolds #Hypersurface #Quintic function #Type (biology) #math.AG #msc:14M10

paper · pdf · doi:10.1007/s00208-009-0376-y

published in Mathematische Annalen 345(3), 731-748 (Springer Nature) · 14 pages

openalex publication_date 2009/05/27 · arxiv created 2010/05/21 · arxiv updated 2010/05/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface X⊂ \bbP⁴ of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in \bbP⁴. We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.

Citations

• Arithmetically Cohen–Macaulay bundles on complete intersection varieties of sufficiently high multidegree
• Vector Bundles on the Punctured Spectrum of a Local Ring