Submanifolds with ample normal bundles and a conjecture of Hartshorne

Details Submanifolds with ample normal bundles and a conjecture of Hartshorne Submanifolds with ample normal bundles and a conjecture of Hartshorne

2008-04-07

arxiv.org/abs/0804.1023v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

The Hartshorne conjecture predicts that two submanifolds X and Y in a projective manifold Z with ample normal bundles meets as soon as dim X + dim Y is at least dim Z. We mostly assume slightly stronger that one of the normal bundles is positive in the sense of Griffiths. We observe that the conjecture holds generically, relate it to question on cones of cycles and verify it in various cases.

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