33 research outputs found
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
Nestings of rational homogeneous varieties
In this paper we study the existence of sections of universal bundles on
rational homogeneous varieties -- called nestings -- classifying them
completely in the case in which the Lie algebra of the automorphism group of
the variety is simple of classical type. In particular we show that, under this
hypothesis, nestings do not exist unless there exists a proper algebraic
subgroup of the automorphism group acting transitively on the base variety.Comment: Major revision of the exposition. To appear in Tranformation Group
Rank two Fano bundles on G(1,4)
We classify rank two Fano bundles over the Grassmannian of lines \G(1,4).
In particular we show that the only non-split rank two Fano bundle over
\G(1,4) is, up to a twist, the universal quotient bundle \cQ. This
completes the classification of rank two Fano bundles over Grassmannians of
lines
Geometric realizations of birational transformations via -actions
In this paper we study varieties admitting torus actions as geometric
realizations of birational transformations. We present an explicit construction
of these geometric realizations for a particular class of birational
transformations, and study some of their geometric properties, such as their
Mori, Nef and Movable cones
Chow quotients of -actions
Given an action of the one-dimensional torus on a projective variety, the
associated Chow quotient arises as a natural parameter space of invariant
-cycles, which dominates the GIT quotients of the variety. In this paper we
explore the relation between the Chow and the GIT quotients of a variety,
showing how to construct explicitly the former upon the latter via successive
blowups under suitable assumptions. We also discuss conditions for the
smoothness of the Chow quotient, and present some examples in which it is
singular.Comment: 29 pages, 4 figure