On second fundamental forms of projective varieties Academic Article uri icon

abstract

  • The projective second fundamental form at a generic smooth point x of a subvariety Xn of projective space ℂℙn+a may be considered as a linear system of quadratic forms |II|x on the tangent space TxX. We prove this system is subject to certain restrictions (4.1), including a bound on the dimension of the singular locus of any quadric in the system |II|x. (The only previously known restriction was that if X is smooth, the singular locus of the entire system must be empty). One consequence of (4.1) is that smooth subvarieties with 2(a-1)

author list (cited authors)

  • Landsberg, J. M.

citation count

  • 14

publication date

  • December 1994