On the embedding of 1-convex manifolds with 1-dimensional exceptional sets.
On the fundamental group of the fixed points of an unipotent action.
On the Holonomic Systems of Linear Differential Equations, II.
On the Homology of Intersections of Complex Projective Manifolds.
On the intersection product of analytic cycles
We prove that the generalized index of intersection of an analytic set with a closed submanifold (Thm. 4.3) and the intersection product of analytic cycles (Thm. 5.4), which are defined in [T₂], are intrinsic. We define the intersection product of analytic cycles on a reduced analytic space (Def. 5.8) and prove a relation of its degree and the exponent of proper separation (Thm. 6.3).
On the Łojasiewicz exponent for analytic curves
An effective formula for the Łojasiewicz exponent for analytic curves in a neighbourhood of 0 ∈ ℂ is given.
On the Łojasiewicz exponent of the gradient of a holomorphic function
The Łojasiewicz exponent of the gradient of a convergent power series h(X,Y) with complex coefficients is the greatest lower bound of the set of λ > 0 such that the inequality holds near for a certain c > 0. In the paper, we give an estimate of the Łojasiewicz exponent of grad h using information from the Newton diagram of h. We obtain the exact value of the exponent for non-degenerate series.
On the Topology of Complex Projective Manifolds.
On 'Type' Conditions for Generic Real Submanifolds of Cn.
Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.
The local Phragmén-Lindelöf condition for analytic varieties in complex n-space was introduced by Hörmander and plays an important role in various areas of analysis. Recently, new necessary geometric properties for a variety satisfying this condition were derived by the present authors. These results are now applied to investigate the homogeneous polynomials P with real coefficients that are stable in the following sense: Whenever f is a holomorphic function that is defined in some neighborhood...
Problème du bord dans l'espace projectif complexe
Nous démontrons qu’une sous-variété réelle de dimension et maximalement complexe d’un ouvert -linéairement concave de est le bord d’un sous-ensemble analytique de dimension de si et seulement s’il existe un sous-ensemble -générique de tel que pour tout l’intersection soit le bord d’une surface de Riemann (pour , est -générique si et seulement s’il n’est pas inclus dans une réunion dénombrable d’hyperplans de ). Ce théorème généralise le théorème de Wermer-Harvey-Lawson...
Propriétés différentielles locales des ensembles analytiques
Pseudoconvexity Properties of Complements of Analytic Subvarieties.
q-Completeness of Subsets in Complex Projective Space.
q-konvexe Restmengen in kompakten komplexen Mannigfaltigkeiten.
Quotients of Analytic Sheaves (With Application to the Generic Local Ring of an Analytic Subset at a Point).
Regularity of varieties in strictly pseudoconvex domains.
We prove a theorem on the boundary regularity of a purely p-dimensional complex subvariety of a relatively compact, strictly pseudoconvex domain in a Stein manifold. Some applications describing the structure of the polynomial hull of closed curves in Cn are also given.
Relativexzeptionelle analytische Mengen.
Remarks on the generalized index of an analytic improper intersection
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...
Richtungsuniformisierung bei analytischen Mengen.