Normal bundles of rational curves in projective spaces

Details Normal bundles of rational curves in projective spaces Normal bundles of rational curves in projective spaces

2003-10-05

arxiv.org/abs/math/0310054v1

Mathematics

Algebraic Geometry

42 pages

Scientific paper

We determine the splitting (isomorphism) type of the normal bundle of a
generic genus-0 curve with 1 or 2 components in any projective space, as well
as the (sometimes nontrivial) way the bundle deforms locally with a general
deformation of the curve. We deduce an enumerative formula for divisorial loci
of smooth rational curves whose normal bundle is of non-generic splitting type.

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