On Bergman completeness of pseudoconvex Reinhardt domains
On b-function, spectrum and rational singularity.
On Bloch's Conjecture.
On Bloch-type functions with Hadamard gaps.
On blowing up versal discriminants
It is well-known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle for analytic triviality of an unfolding or deformation along the moduli. The goal of this paper is to describe the versal discriminant of and singularities basing on the fact that the deformations of these singularities may be obtained as blowing ups of certain deformations...
On Bochner-Martinelli residue currents and their annihilator ideals
We study the residue current of Bochner-Martinelli type associated with a tuple of holomorphic germs at , whose common zero set equals the origin. Our main results are a geometric description of in terms of the Rees valuations associated with the ideal generated by and a characterization of when the annihilator ideal of equals .
On boundary behaviour of Bergman kernel function for plane domains and their Cartesian products
On boundary behaviour of the Bergman projection on pseudoconvex domains
It is shown that on strongly pseudoconvex domains the Bergman projection maps a space of functions growing near the boundary like some power of the Bergman distance from a fixed point into a space of functions which can be estimated by the consecutive power of the Bergman distance. This property has a local character. Let Ω be a bounded, pseudoconvex set with C³ boundary. We show that if the Bergman projection is continuous on a space defined by weighted-sup seminorms and equipped with the topology...
On boundary Hilbert differential complexes
On Bounded Holomorphic Interpolation in Several Variables.
On branches at infinity of a pencil of polynomials in two complex variables
Let F ∈ ℂ[x,y]. Some theorems on the dependence of branches at infinity of the pencil of polynomials f(x,y) - λ, λ ∈ ℂ, on the parameter λ are given.
On Brody and entire curves
We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.
On c-actions on compact complex manifolds with many compact orbits.
On Calabi's conjecture for complex surfaces with positive first Chern class.
On canonical homotopy operators for ∂ in Fock type spaces in Cn.
We show that a certain solution operator for ∂ in a space of forms square integrable against e-|z|2 is canonical, i.e., that it gives the minimal solution when applied to a ∂-closed form, and gives zero when applied to a form orthogonal to Ker ∂.As an application, we construct a canonical homotopy operator for i∂∂.
On certain groups of holomorphic maps
On certain rigid fibered Calabi-Yau threefolds.
On classification of real singularities.
On Clifford's theorem for rank-3 bundles.
In this paper we obtain bounds on h0(E) where E is a semistable bundle of rank 3 over a smooth irreducible projective curve X of genus g ≥ 2 defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability s1(E), s2(E). We show also that in some cases the bounds are best possible. These results extend recent work of J. Cilleruelo and I. Sols for bundles of rank 2.