Normal Bundles of Rational Curves in Projective Spaces

By Z. Ran. 2003

65 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cc6d580b700797e0b981f3145ac5198c5c2f54d3

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In Geometry and Topology

1. Izzet Coskun
2. Eric Riedl

In Mathematical Physics

1. Izzet Coskun
2. Eric Riedl

Citations in the corpus

• Normal bundles of rational curves in projective space (2016, background): “xists a rational curve f: P1 → Pn with ordinary singularities such that Nf = ⊕n−1 i=1 O(e+bi). In particular, the general smooth rational curve in Pn has balanced normal bundle. 5 Other authors, (see [Ra07]) have studied the generic splitting type of normal bundles of rational curves and described t”