On a Generalization of the Hopf Fibration, III. (Subvarieties in the C-Spaces).
On complete intersections
We construct closed complex submanifolds of which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of .
On Dolbeault Cohomology and Envelopes of Holomorphy.
On improper isolated intersection in complex analytic geometry
On irreducible components of a Weierstrass-type variety
We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.
On Noether and strict stability, Hilbert exponent, and relative Nullstellensatz
Conditions characterizing the membership of the ideal of a subvariety arising from (effective) divisors in a product complex space Y × X are given. For the algebra of relative regular functions on an algebraic variety V, the strict stability is proved, in the case where Y is a normal space, and the Noether stability is established under a weakened condition. As a consequence (for both general and complete intersections) a global Nullstellensatz is derived for divisors in , respectively, . Also...
On proper discs in complex manifolds
Let be a complex manifold of dimension at least which has an exhaustion function whose Levi form has at each point at least strictly positive eigenvalues. We construct proper holomorphic discs in through any given point and in any given direction.
On the compactification problem for Stein surfaces
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.