Lines on projective varieties Academic Article uri icon

abstract

  • I prove two theorems: Let Xn ⊂ ℙn+1be a hypersurface and let x ε 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. A variety X is said to be covered by lines if there exist a finite number of lines in X passing through a general point. Let Xn ⊂ ℙM be a variety covered by lines. Then there are at most n! lines passing through a general point of X.

author list (cited authors)

  • Landsberg, J. M.

citation count

  • 3

publication date

  • September 2003