Families of singular rational curves

Details Families of singular rational curves Families of singular rational curves

2000-04-05

arxiv.org/abs/math/0004023v2

Mathematics

Algebraic Geometry

Reason for resubmission: improved exposition

Scientific paper

Let X be a projective variety which is covered by a family of rational curves of minimal degree. The classic bend-and-break argument of Mori asserts that if x and y are two general points, then there are at most finitely many curves in that family which contain both x and y. In this work we shed some light on the question as to whether two sufficiently general points actually define a unique curve. As an immediate corollary to the results of this paper, we give a characterization of projective spaces which improves on the known generalizations of Kobayashi-Ochiai's theorem.

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