Geodesic
Complete Families of Linearly Non-degenerate Rational Curves
Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 430-441

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DOI

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.
DOI : 10.4153/CMB-2011-021-2
Mots-clés : 14N05, 14H10 
DeLand, Matthew. Complete Families of Linearly Non-degenerate Rational Curves. Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 430-441. doi: 10.4153/CMB-2011-021-2
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     author = {DeLand, Matthew},
     title = {Complete {Families} of {Linearly} {Non-degenerate} {Rational} {Curves}},
     journal = {Canadian mathematical bulletin},
     pages = {430--441},
     year = {2011},
     volume = {54},
     number = {3},
     doi = {10.4153/CMB-2011-021-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-021-2/}
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