The purpose of this paper is to give a characterization of the relative tangent cone of two analytic curves in ${ℂ}^m$ with an isolated intersection.

We give a characterization of the relative tangent cone of an analytic curve and an analytic set with an improper isolated intersection. Moreover, we present an effective computation of the intersection multiplicity of a curve and a set with s-metrization.

 Abstract. The characterization of hyperbolic embeddability of relatively compact subspaces of a complex space in terms of extension of holomorphic maps from the punctured disc and of limit complex lines is given.

We give some criteria for the equisingularity of families of affine plane curves.

The aim of the paper is to establish some results on pluripolar hulls and to define pluripolar hulls of certain graphs.

In this paper we study the balanced metrics on some Hartogs triangles of exponent $\gamma \in {\mathbb{Z}}^{+}$, i.e., $${\Omega }_n\left(\gamma \right)=\{z=(z_1,\cdots ,z_n)\in {ℂ}^n:|z_1{|}^{1/\gamma }<|z_2|<\cdots <|z_n|<1\}$$ equipped with a natural Kähler form ${\omega }_{g\left(\mu \right)}:=\frac{1}{2}(i/\pi )\partial \overline{\partial }{\Phi }_n$ with $${\Phi }_n\left(z\right)=-{\mu }_{1}ln\left(\right|z_2{|}^{2\gamma }-\left|z_1{|}^2\right)-\sum _{i=2}^{n-1}{\mu }_{i}ln\left(\right|z_{i+1}{|}^2-\left|z_i{|}^2\right)-{\mu }_{n}ln(1-|z_n{|}^2),$$ where $\mu =({\mu }_1,\cdots ,{\mu }_n)$, ${\mu }_i>0$, depending on $n$ parameters. The purpose of this paper is threefold. First, we compute the explicit expression for the weighted Bergman kernel function for $({\Omega }_n\left(\gamma \right),g\left(\mu \right))$ and we prove that $g\left(\mu \right)$ is balanced if and only if ${\mu }_1>1$ and $\gamma {\mu }_1$ is an integer, ${\mu }_i$ are integers such that ${\mu }_i\ge 2$ for all $i=2,...,n-1$, and ${\mu }_n>1$. Second, we prove that $g\left(\mu \right)$ is Kähler-Einstein if and only if ${\mu }_1={\mu }_2=\cdots ={\mu }_n=2\lambda$, where $\lambda$ is a nonzero...

We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be $C^{\infty }$-smoothly extended to the boundary.

This article continues the investigation of the analytic intersection algorithm from the perspective of deformation to the normal cone, carried out in the previous papers of the author [7, 8, 9]. The main theorem asserts that, given an analytic set V and a linear subspace S, every collection of hyperplanes, admissible with respect to an algebraic bicone B, realizes the generalized intersection index of V and S. This result is important because the conditions for a collection of hyperplanes to be...

This paper is an outgrowth of a paper by the first author on a generalized Hartogs Lemma. We complete the discussion of the nonlinear ∂̅ problem ∂f/∂z̅ = ψ(z,f(z)). We also simplify the proofs by a different choice of Banach spaces of functions.

We prove the invariance of hyperbolic imbeddability under holomorphic fiber bundles with compact hyperbolic fibers. Moreover, we show an example concerning the relation between the Kobayashi relative intrinsic pseudo-distance of a holomorphic fiber bundle and the one in its base.

On caractérise les ouverts d’homologie d’un produit dénombrable de droites réelles ou complexes.