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Complete Families of Linearly Non-degenerate Rational Curves

Published online by Cambridge University Press:  20 November 2018

Matthew DeLand
Matthew DeLand*
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10025, U.S.A. e-mail: deland@math.columbia.edu
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Abstract

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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.

Keywords

14N0514H10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011 , pp. 430 - 441
Copyright
Copyright © Canadian Mathematical Society 2011

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