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Normal bundles of rational curves in projective spaces

Ziv Ran
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Abstract

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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Ziv Ran. 2003-10-05. Normal bundles of rational curves in projective spaces. https://arxiv.org/abs/math/0310054

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