Families of singular rational curves

2000/04/05 by Stefan Kebekus, Kebekus, Stefan
Mathematics · #14C15 #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C15 #msc:14J45

paper · pdf · doi:10.48550/arxiv.math/0004023

Reason for resubmission: improved exposition

arxiv created 2000/06/06 · arxiv updated 2009/11/30

Abstract

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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