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Complete Families of Linearly Non-degenerate Rational Curves

Open Access article
 Printed: Sep 2011
  • Matthew DeLand,
    Department of Mathematics, Columbia University, New York, NY 10025, U.S.A.
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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, 14H10 show english descriptions Projective techniques [See also 51N35]
Families, moduli (algebraic)
14N05 - Projective techniques [See also 51N35]
14H10 - Families, moduli (algebraic)

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