169 research outputs found
A note on the birational geometry of tropical line bundles
Given a closed subvariety Y of a n-dimensional torus, we study how the
tropical line bundles of Trop(Y) can be induced by line bundles living on a
tropical compactification of Y in a toric variety, following the construction
of Jenia Tevelev. We then consider the general structure with respect to the
Zariski--Riemann space.Comment: Version
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
Extremal rays of non-integral -length
Let be a smooth complex projective variety and let be a line bundle on it.
We describe the structure of the pre-polarized manifold for non integral values of the invariant , where is a minimal curve of an extremal ray on such that
Extremal rays of non-integral -length
Let be a smooth complex projective variety and let be a line bundle
on it. We describe the structure of the pre-polarized manifold for non
integral values of the invariant ,
where is a minimal curve of an extremal ray
on such that .Comment: 13 page
On Fano manifolds with an unsplit dominating family of rational curves
We study Fano manifolds admitting an unsplit dominating family of
rational curves and we prove that the Generalized Mukai Conjecture holds if
has pseudoindex or dimension . We also show that
this conjecture is true for all Fano manifolds with .Comment: 11 pages. arXiv admin note: substantial text overlap with
arXiv:0905.438
Manifolds covered by lines and extremal rays
Let be a smooth complex projective variety and let H \in \pic(X) be an
ample line bundle. Assume that is covered by rational curves with degree
one with respect to and with anticanonical degree greater than or equal to
. We prove that there is a covering family of such curves whose
numerical class spans an extremal ray in the cone of curves \cone(X).Comment: Major revision, to appear in Canadian Mathematical Bulleti
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