Complete families of linearly non-degenerate rational curves

Details Complete families of linearly non-degenerate rational curves Complete families of linearly non-degenerate rational curves

2007-10-30

arxiv.org/abs/0710.5713v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We prove that a complete family of linearly non-degenerate rational curves of degree $e > 2$ in $\mathbb{P}^n$ has at most $n-1$ moduli. For $e = 2$ we prove that such a family has at most $n$ moduli. It is unknown whether or not this is the best possible result. The general method involves exhibiting a map from the base of a family $X$ to the Grassmaninian of $e$-planes in $\mathbb{P}^n$ and analyzing the resulting map on cohomology.

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