4,909 research outputs found
Tower of coverings of quasi-projective varieties
The main goal of this article is to relate asymptotic geometric properties on
a tower of coverings of a non-compact K\"ahler manifold of finite volume with
reasonable geometric assumptions to its universal covering. Applicable examples
include moduli spaces of hyperbolic punctured Riemann surfaces and Hermitian
locally symmetric spaces of finite volume
Hermitian structures on the derived category of coherent sheaves
The main objective of the present paper is to set up the theoretical basis
and the language needed to deal with the problem of direct images of hermitian
vector bundles for projective non-necessarily smooth morphisms. To this end, we
first define hermitian structures on the objects of the bounded derived
category of coherent sheaves on a smooth complex variety. Secondly we extend
the theory of Bott-Chern classes to these hermitian structures. Finally we
introduce the category \oSm_{\ast/\CC} whose morphisms are projective
morphisms with a hermitian structure on the relative tangent complex
A characterization of Hermitian varieties as codewords
It is known that the Hermitian varieties are codewords in the code defined by
the points and hyperplanes of the projective spaces . In finite
geometry, also quasi-Hermitian varieties are defined. These are sets of points
of of the same size as a non-singular Hermitian variety of
, having the same intersection sizes with the hyperplanes of
. In the planar case, this reduces to the definition of a unital. A
famous result of Blokhuis, Brouwer, and Wilbrink states that every unital in
the code of the points and lines of is a Hermitian curve. We prove
a similar result for the quasi-Hermitian varieties in , ,
as well as in , prime, or , prime, and
Unitary grassmannians
We study projective homogeneous varieties under an action of a projective
unitary group (of outer type). We are especially interested in the case of
(unitary) grassmannians of totally isotropic subspaces of a hermitian form over
a field, the main result saying that these grassmannians are 2-incompressible
if the hermitian form is generic. Applications to orthogonal grassmannians are
provided.Comment: 25 page
On reduction of moduli schemes of abelian varieties with definite quaternion multiplications
In this paper we make an initial study on type D moduli spaces in positive
characteristic , where we allow ramified in the definite
quaternion algebra. We classify the isogeny classes of -divisible groups
with additional structures in question. We also study the reduction of the type
moduli spaces of minimal rank.Comment: 57 pages, to appear in Annales de l'Institut Fourier (Grenoble
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