Manifolds covered by lines and the Hartshorne Conjecture for quadratic manifolds

Abstract

Small codimensional embedded manifolds defined byequations 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.

11 pages; this was part of math.AG/0909.2763, which has been withdrawn and divided into two parts. To appear in American Journal of Math. (accepted October 2011)

Cited by in corpus (4)

• Quadro-quadric special birational transformations of projective spaces
• K-theory, LQEL manifolds and Severi varieties
• Euler-symmetric complete intersection in projective space
• Remarks on defective Fano manifolds