Complete intersection subvarieties of general hypersurfaces

Endre Szabó

Vol. 175 (1996), No. 1, 271–294

DOI: 10.2140/pjm.1996.175.271

Abstract

In this paper we classify the nontrivial complete intersection curves on a general hypersurface of large enough degree. We prove, that in principle, one can classify nontrivial complete intersection curves on hypersurfaces with relatively small degree as well, and give a recipe for doing so. We also estimate the codimension of the components of the Noether-Lefschetz locus corresponding to complete intersection curves. Similar theorems hold for higher dimensional complete intersection subvarieties.

Mathematical Subject Classification 2000

Primary: 14M10

Milestones

Received: 24 January 1994

Published: 1 September 1996