Compact subvarieties with ample normal bundles, algebraicity and cones of cycles

Details Compact subvarieties with ample normal bundles, algebraicity and cones of cycles Compact subvarieties with ample normal bundles, algebraicity and cones of cycles

2011-06-22

arxiv.org/abs/1106.4433v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

In this note we study two features of submanifolds (subvarieties) with ample
normal bundles in a compact K\"ahler manifold X. First, we study how algebraic
X can be, i.e. we investigate the algebraic dimension. Second, we study curves
with ample normal bundles in case X is projective. We prove in various cases
that the class of the curve is in the interior of the Mori cone.

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