Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture

Details Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture

2009-09-15

arxiv.org/abs/0909.2763v2

Mathematics

Algebraic Geometry

21 pages; a wrong statement in Theorem 2.4 in the non-quadratic case corrected. All the other results remain unaltered. Minor

Scientific paper

Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds. Using the geometry of the variety of lines through a general point, we characterize scrolls among dual defective manifolds. This leads to an optimal bound for the dual defect, which improves results due to Ein. We discuss our conjecture that every dual defective manifold with cyclic Picard group should also be secant defective, of a very special type, namely a local quadratic entry locus variety.

Affiliated with

Also associated with

No associations

Rating

Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture 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 Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Manifolds covered by lines, defective manifolds and a restricted Hartshorne Conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-555836