Stein domains and branched shadows of 4-manifolds

We provide sufficient conditions assuring that a suitably decorated 2-polyhedron can be thickened to a compact four-dimensional Stein domain. We also study a class of flat polyhedra in 4-manifolds and find conditions assuring that they admit Stein, compact neighborhoods. We base our calculations on Turaev’s shadows suitably “smoothed”; the conditions we find are purely algebraic and combinatorial. Applying our results, we provide examples of hyperbolic 3-manifolds admitting “many” positive and negative Stein fillable contact structures, and prove a four-dimensional analog of Oertel’s result on incompressibility of surfaces carried by branched polyhedra.      

Cousin I condition and Stein spaces

Here we give a few n-dimensional extensions of a recent result of M. Abe concerning a Cousin I characterization of two-dimensional Stein manifolds.     

Stein structures and holomorphic mappings

We prove that every continuous map from a Stein manifold X to a complex manifold Y can be made holomorphic by a homotopic deformation of both the map and the Stein structure on X. In the absence of topological obstructions, the holomorphic map may be chosen to have pointwise maximal rank. The analogous result holds for any compact Hausdorff family of maps, but it fails in general for a noncompact family. Our main results are actually proved for smooth almost complex source manifolds (X,J) with the correct handlebody structure. The paper contains another proof of Eliashberg’s (Int J Math 1:29–46, 1990) homotopy characterization of Stein manifolds and a slightly different explanation of the construction of exotic Stein surfaces due to Gompf (Ann Math 148(2): 619–693, 1998; J Symplectic Geom 3:565–587, 2005).      

Fundamental domains in Lorentzian geometry

We consider a discrete subgroup Γ of the simply connected Lie group of finite level, i.e. the subgroup intersects the centre of in a subgroup of finite index, this index is called the level of the group. The Killing form induces a Lorentzian metric of constant curvature on the Lie group . The discrete subgroup Γ acts on by left translations. We describe the Lorentz space form by constructing a fundamental domain F for Γ. We want F to be a polyhedron with totally geodesic faces. We construct such F for all Γ satisfying the following condition: The image of Γ in PSU(1,1) has a fixed point u in the unit disk of order larger than the index of Γ. The construction depends on the group Γ and on the orbit Γ(u) of the fixed point u.      

Stein estimation under elliptical distributions

In a subclass of elliptical distributions, Stein estimators are robust in estimating the mean vector and the regression parameters in a linear regression model. Unbiased estimates of bias and risk are also given for the regression model.     

The Moduli of Quasi-Homogeneous Stein Surface Singularities

In this article we study good ℂ^* actions on Stein surfaces and we construct their moduli by means of the resolution data of the dicritical singularity of the action. We also classify ℂ^* transversal actions around a Riemann surface embedded in a two dimensional manifold.      

Stein domains in complex surfaces

Let S be a closed connected real surface and π: S→X a smooth embedding or immersion of S into a complex surface X. We denote by I(π) (resp. by I_±(π) if S is oriented) the number of complex points of π (S)∪X counted with algebraic multiplicities. Assuming that I(π)≤0 (resp. I_±(π)≤0 if S is oriented) we prove that π can be C⁰ approximated by an isotopic immersion π₁: S→X whose image has a basis of open Stein neighborhood in X which are homotopy equivalents to π₁ (S). We obtain precise results for surfaces in and find an immersed symplectic sphere in with a Stein neighborhood.     

Stein estimation of Poisson process intensities

We construct superefficient estimators of Stein type for the intensity parameter λ > 0 of a Poisson process, using integration by parts and superharmonic functionals on the Poisson space.      

Cohomology of locally q-complete sets in Stein manifolds

We prove that if X is a Stein complex manifold of dimension n and Ω???X a locally q-complete open set in X with q?≤?n?2, then the cohomology groups H ^p (Ω , OΩ) vanish if p?≥?q and OΩ is the sheaf of germs of holomorphic functions on Ω.     

Coherent algebraic sheaves in real algebraic geometry

Summary In the following paper we give examples of vector bundlesF→X defined on a regular, compact, connected affine varietyX such thatF has no algebraic structure.

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Riassunto Nel presente lavoro si danno esempi di fibrati vettorialiF→X, definiti su varietà affini, regolari, compatte, connesseX che non ammettono struttura algebrica.

     

基于Stein方法的均衡分布的Berry-Esseen界

受Shao和Su(2006)的启发,获得了均衡分布的Berry-Esseen界,定理的证明基于Stein方法.     

Bloch spaces on bounded symmetric domains in complex Banach spaces

We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

An algebra of Stein operators

We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our results are valid for a wide class of distributions including normal, beta, variance-gamma, generalized gamma and many more. Our operators are kth degree differential operators with polynomial coefficients; they are straightforward to obtain even when the target density bears no explicit handle. As an application, we derive a new formula for the density of the product of k independent symmetric variance-gamma distributed random variables.     

Algebraic geometry over algebraic structures. IV. Equational domains and codomains

We introduce and study equational domains and equational codomains. Informally, an equational domain is an algebra every finite union of algebraic sets over which is an algebraic set; an equational codomain is an algebra every proper finite union of algebraic sets over which is not an algebraic set.     

A geometry characteristic of Banach spaces with c 1-norm

Let E be a Banach space with the cl-norm｜｜·｜｜ in E／{0}, and let S（E） = {e ∈ E： ｜｜e｜｜ = 1}. In this paper, a geometry characteristic for E is presented by using a geometrical construct of S（E）. That is, the following theorem holds： the norm of E is of eI in E／{0} if and only if S（E） is a c1 submanifold of E, with codimS（E） = 1. The theorem is very clear, however, its proof is non-trivial, which shows an intrinsic connection between the continuous differentiability of the norm ｜｜·｜｜ in E／{0} and differential structure of S（E）.     

Deformation quantization in algebraic geometry

We study deformation quantizations of the structure sheaf O_X of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of O_X (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.     

The Berry-Esseen bound for identically distributed random variables by Stein method

In this paper, we obtain the Berry-Esseen bound for identically distributed random variables by Stein method. The results obtained generalize the results of Shao and Su (2006) and Stein (1986).