28 research outputs found
Contact Moishezon threefolds with second Betti number one
We prove that the only contact Moishezon threefold having second Betti number
equal to one is the projective space.Comment: 5 pages. v2: exposition improved as suggested by the referee. To
appear in Archiv der Mat
Cohomological characterizations of projective spaces and hyperquadrics
We confirm Beauville's conjecture that claims that if the p-th exterior power
of the tangent bundle of a smooth projective variety contains the p-th power of
an ample line bundle, then the variety is either the projective space or the
p-dimensional quadric hypersurface.Comment: Added Lemma 2.8 and slightly changed proof of Lemma 6.2 to make them
apply for torsion-free sheaves and not only to vector bundle
Differential Forms on Log Canonical Spaces
The present paper is concerned with differential forms on log canonical
varieties. It is shown that any p-form defined on the smooth locus of a variety
with canonical or klt singularities extends regularly to any resolution of
singularities. In fact, a much more general theorem for log canonical pairs is
established. The proof relies on vanishing theorems for log canonical varieties
and on methods of the minimal model program. In addition, a theory of
differential forms on dlt pairs is developed. It is shown that many of the
fundamental theorems and techniques known for sheaves of logarithmic
differentials on smooth varieties also hold in the dlt setting.
Immediate applications include the existence of a pull-back map for reflexive
differentials, generalisations of Bogomolov-Sommese type vanishing results, and
a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared
in Publications math\'ematiques de l'IH\'ES. The final publication is
available at http://www.springerlink.co
Holomorphic symplectic geometry: a problem list
A list of open problems on holomorphic symplectic, contact and Poisson
manifolds
Positivity of relative canonical bundles and applications
Given a family of canonically polarized manifolds, the
unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the
relative canonical bundle . We use a global elliptic
equation to show that this metric is strictly positive on , unless
the family is infinitesimally trivial.
For degenerating families we show that the curvature form on the total space
can be extended as a (semi-)positive closed current. By fiber integration it
follows that the generalized Weil-Petersson form on the base possesses an
extension as a positive current. We prove an extension theorem for hermitian
line bundles, whose curvature forms have this property. This theorem can be
applied to a determinant line bundle associated to the relative canonical
bundle on the total space. As an application the quasi-projectivity of the
moduli space of canonically polarized varieties
follows.
The direct images , , carry natural hermitian metrics. We prove an
explicit formula for the curvature tensor of these direct images. We apply it
to the morphisms that are induced by the Kodaira-Spencer map and obtain a differential
geometric proof for hyperbolicity properties of .Comment: Supercedes arXiv:0808.3259v4 and arXiv:1002.4858v2. To appear in
Invent. mat
Almost homogeneous projective 3-folds
SIGLEAvailable from TIB Hannover: RR 5293(16) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman