Normal bundles of rational curves in projective spaces

2003/10/05 by Ziv Ran, Ran, Ziv · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Tensor decomposition and applications #math.AG #msc:14N10

paper · pdf · doi:10.48550/arxiv.math/0310054

42 pages

arxiv created 2003/10/05 · arxiv updated 2009/12/01

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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• Restricted tangent bundle of rational curves on projective hypersurfaces

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