Lines on algebraic varieties
Abstract
A variety $X$ is covered by lines if there exist a finite number of lines contained in $X$ passing through each general point. I prove two theorems. Theorem 1:Let $X^n\subset P^M$ be a variety covered by lines. Then there are at most $n!$ lines passing through a general point of $X$. Theorem 2:Let $X^n\subsetP^{n+1}$ be a hypersurface and let $x\in X$ be a general point. If the set of lines having contact to order $k$ with $X$ at $x$ is of dimension greater than expected, then the lines having contact to order $k$ are actually contained in $X$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2001
 arXiv:
 arXiv:math/0111039
 Bibcode:
 2001math.....11039L
 Keywords:

 Algebraic Geometry
 EPrint:
 3 pages