350 research outputs found
Manifolds with nef cotangent bundle
Generalising a classical theorem by Ueno, we prove structure results for
manifolds with nef or semiample cotangent bundle.Comment: 9 pages, changed metadat
M-regularity of the Fano surface
Let be a principally polarised abelian variety, and let Y be a
subvariety. Pareschi and Popa conjectured that Y has minimal cohomology class
if and only if the structure sheaf of Y satisfies a property that they call
M-regularity.
Let now X be a smooth cubic threefold. By a classical result due to Clemens
and Griffiths, its intermediate Jacobian J(X) is a principally polarised
abelian variety; furthermore the Fano surface of lines on X can be embedded in
J(X) and has minimal cohomology class. In this short note we show that its
structure sheaf is M-regular.Comment: 5 pages, changed metadat
Uniruled varieties with split tangent bundle
Beauville asked if a compact K\"ahler manifold with split tangent bundle has
a universal covering that is a product of manifolds. We use Mori theory and
elementary results about holomorphic foliations to study this problem for
projective uniruled varieties. In particular we obtain an affirmative answer
for rationally connected varieties in any dimension and uniruled varieties in
dimension 4.Comment: changed metadat
Geometry of Brill-Noether loci on Prym varieties
Given the Prym variety of an \'etale double cover one can define analogues of
the classical Brill-Noether loci on Jacobians of curves. Recent work by Lahoz
and Naranjo shows that the Brill-Noether locus completely determines the
covering. In this paper we describe the singular locus and the irreducible
components of .Comment: 19 pages, changed metadat
Adjoint -classes on threefolds
We answer a question of Filip and Tosatti concerning a basepoint-free theorem
for transcendental -classes on threefolds.Comment: 8 page
The structure of uniruled manifolds with split tangent bundle
In this paper we show that a uniruled manifold with a split tangent bundle
admits almost holomorphic fibrations that are related to the splitting. We
analyse these fibrations in detail in several special cases, this yields new
results about the integrability of the direct factors and the universal
covering of the manifold.Comment: 14 page
Non-algebraic compact K\"ahler threefolds admitting endomorphisms
We classify non-algebraic compact K\"ahler threefolds admitting an
endomorphism of degree at least two.Comment: 39 pages, changed metadat
Algebraic integrability of foliations with numerically trivial canonical bundle
Given a reflexive sheaf on a mildly singular projective variety, we prove a
flatness criterion under certain stability conditions. This implies the
algebraicity of leaves for sufficiently stable foliations with numerically
trivial canonical bundle such that the second Chern class does not vanish.
Combined with the recent work of Druel and Greb-Guenancia-Kebekus this
establishes the Beauville-Bogomolov decomposition for minimal models with
trivial canonical class.Comment: 20 pages, removed an assumption from Thm.1.
Quasi-lines and their degenerations
In this paper we study the structure of manifolds that contain a quasi-line
and give some evidence towards the fact that the irreducible components of
degenerations of the quasi-line should determine the Mori cone. We show that
the minimality with respect to a quasi-line yields strong restrictions on fibre
space structures of the manifold.Comment: 20 pages, changed metadat
Singularities of varieties admitting an endomorphism
Let X be a normal variety such that is Q-Cartier, and let be a finite surjective morphism of degree at least two. We
establish a close relation between the irreducible components of the locus of
singularities that are not log-canonical and the dynamics of the endomorphism
f. As a consequence we prove that if X is projective and f polarised, then X
has at most log-canonical singularities.Comment: 15 pages, changed metadat
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