A Noether-Lefschetz theorem for varieties of r-planes in complete intersections

Details A Noether-Lefschetz theorem for varieties of r-planes in complete intersections A Noether-Lefschetz theorem for varieties of r-planes in complete intersections

2010-10-25

arxiv.org/abs/1010.5210v1

Mathematics

Algebraic Geometry

Comments welcome

Scientific paper

Let X be a very general complete intersection in complex projective space and we denote by $F_r(X)$ the variety of r-planes in X, for $r\geq 1$. We show that the Picard number of $F_r(X)$ is 1, as soon as $\dim F_r(X)\geq 2$, except when X is a quadric of dimension 2r or 2r+2, or X is a complete intersection of two quadrics of dimension 2r+2. We also apply this result to determine the cohomology class of the variety of planes of a cubic fivefold contained (by the Abel-Jacobi map) in the intermediate Jacobian.

Affiliated with

Also associated with

No associations

Rating

A Noether-Lefschetz theorem for varieties of r-planes in complete intersections does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Noether-Lefschetz theorem for varieties of r-planes in complete intersections, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Noether-Lefschetz theorem for varieties of r-planes in complete intersections will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-94544