Spaces of rational curves in complete intersections

Details Spaces of rational curves in complete intersections Spaces of rational curves in complete intersections

2011-01-19

arxiv.org/abs/1101.3797v1

Mathematics

Algebraic Geometry

Scientific paper

We prove that the space of smooth rational curves of degree $e$ in a general complete intersection of multidegree $(d_1, ..., d_m)$ in $\PP^n$ is irreducible of the expected dimension if $\sum_{i=1}^m d_i <\frac{2n}{3}$ and $n$ is large enough. This generalizes the results of Harris, Roth and Starr \cite{hrs}, and is achieved by proving that the space of conics passing through any point of a general complete intersection has constant dimension if $\sum_{i=1}^m d_i$ is small compared to $n$.

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