470 research outputs found
Ruled Fano fivefolds of index two
We classify Fano fivefolds of index two which are projectivization of rank
two vector bundles over four dimensional manifolds.Comment: 30 page
Rationally cubic connected manifolds I: manifolds covered by lines
In this paper we study smooth complex projective polarized varieties (X,H) of
dimension n \ge 2 which admit a dominating family V of rational curves of
H-degree 3, such that two general points of X may be joined by a curve
parametrized by V, and such that there is a covering family of rational curves
of H-degree one. Our main result is that the Picard number of these manifolds
is at most three, and that, if equality holds, (X,H) has an adjuction theoretic
scroll structure over a smooth variety
Generalized Mukai conjecture for special Fano varieties
Let X be a Fano variety of dimension n, pseudoindex i_X and Picard number
\rho_X. A generalization of a conjecture of Mukai says that \rho_X(i_X-1)\le n.
We prove that the conjecture holds if: a) X has pseudoindex i_X \ge
\frac{n+3}{3} and either has a fiber type extremal contraction or does not have
small extremal contractions b) X has dimension five.Comment: 19 page
On rank 2 vector bundles on Fano manifolds
In this work we deal with vector bundles of rank two on a Fano manifold
with . We study the nef and pseudoeffective cones of the
corresponding projectivizations and how these cones are related to the
decomposability of the vector bundle. As consequences, we obtain the complete
list of -bundles over that have a second
-bundle structure, classify all the uniform rank two vector
bundles on this class of Fano manifolds and show the stability of
indecomposable Fano bundles (with one exception on ).Comment: Updated version with an issue correcte
Uniform families of minimal rational curves on Fano manifolds
It is a well-known fact that families of minimal rational curves on rational
homogeneous manifolds of Picard number one are uniform, in the sense that the
tangent bundle to the manifold has the same splitting type on each curve of the
family. In this note we prove that certain --stronger-- uniformity conditions
on a family of minimal rational curves on a Fano manifold of Picard number one
allow to prove that the manifold is homogeneous
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