On the variety of rational curves in \({\mathbb{P}}^ n\). (English) Zbl 0649.14016
In this note one defines a stratification of the variety of rational curves in \({\mathbb{P}}^ n\) of given degree in terms of the decomposition of the normal bundle [see D. Eisenbud and A. Van de Ven [Invent. Math. 67, 89-100 (1982; Zbl 0492.14016)] and F. Ghione and G. Sacchiero, Manuscr. Math. 33, 111-128 (1980; Zbl 0496.14021) for the case n=3]. The strata are showed to be irreducible and their dimension is computed.
MSC:
14H10 | Families, moduli of curves (algebraic) |
14N05 | Projective techniques in algebraic geometry |
57N80 | Stratifications in topological manifolds |