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# Complete Families of Linearly Non-degenerate Rational Curves

Published:2011-03-05
Printed: Sep 2011
• Matthew DeLand,
Department of Mathematics, Columbia University, New York, NY 10025, U.S.A.
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## Abstract

We prove that every 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. The general method involves exhibiting a map from the base of a family $X$ to the Grassmannian of $e$-planes in $\mathbb{P}^{n}$ and analyzing the resulting map on cohomology.
 MSC Classifications: 14N05 - Projective techniques [See also 51N35] 14H10 - Families, moduli (algebraic)