10,688 research outputs found
An effective version of a theorem of Kawamata on the Albanese map
This paper is devoted to study the birational properties of the Albanese map.
I generalize a theorem of Kawamata to tell when the Albanese map is surjective
and when it is an algebraic fiber space.Comment: To appear in Communications in Contemporary Mathematics. This is the
final version of the first part of arXiv:0909.397
On the Chow ring of certain rational cohomology tori
Let be an abelian cover from a complex algebraic variety
with quotient singularities to an abelian variety. We show that induces
an isomorphism between the rational cohomology rings
and if and only if induces an isomorphism
between the Chow rings with rational coefficients
and
.Comment: 6 page
A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume
We study the canonical stability index of nonsingular projective varieties of
general type with either large canonical volume or large geometric genus. As
applications of a general extension theorem established in the first part, we
prove some optimal results in dimensions 4 and 5, which are parallel to some
well-known results on surfaces and 3-folds.Comment: Final version, 35 pages, Annales de l'Institut Fourier (to appear
Cohomological rank functions on abelian varieties
Generalizing the continuous rank function of Barja-Pardini-Stoppino, in this
paper we consider cohomological rank functions of -twisted
(complexes of) coherent sheaves on abelian varieties. They satisfy a natural
transformation formula with respect to the Fourier-Mukai-Poincar\'e transform,
which has several consequences. In many concrete geometric contexts these
functions provide useful invariants. We illustrate this with two different
applications, the first one to GV-subschemes and the second one to
multiplication maps of global sections of ample line bundles on abelian
varieties.Comment: 28 pages, minor changes. Final version to appear on Annales Scient.
EN
Varieties with vanishing holomorphic Euler characteristic II
We continue our study on smooth complex projective varieties of maximal
Albanese dimension and of general type satisfying . We
formulate a conjectural characterization of such varieties and prove this
conjecture when the Albanese variety has only three simple factors.Comment: 27 page
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