The homotopy axiom in semialgebraic cohomology.
The Hua system on irreducible Hermitian symmetric spaces of nontube type
Let be an irreducible Hermitian symmetric space of noncompact type. We study a - invariant system of differential operators on called the Hua system. It was proved by K. Johnson and A. Korányi that if is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube type. In...
The hypercomplex quotient and the quaternionic quotient.
The ideal boundary of a domain in
The image of a finely holomorphic map is pluripolar
We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.
The incidence class and the hierarchy of orbits
R. Rimányi defined the incidence class of two singularities η and ζ as [η]|ζ, the restriction of the Thom polynomial of η to ζ. He conjectured that (under mild conditions) [η]|ζ ≠ 0 ⇔ ζ ⊂ . Generalizing this notion we define the incidence class of two orbits η and ζ of a representation. We give a sufficient condition (positivity) for ζ to have the property that [η]|ζ ≠ 0 ⇔ ζ ⊂ for any other orbit η. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity...
The index of a holymorphic flow with an isolated singularity.
The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant
Given a real analytic vector field tangent to a hypersurface with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra associated with the singularity of the vector field on . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation of...
The index of analytic vector fields and Newton polyhedra
We prove that if f:(ℝⁿ,0) → (ℝⁿ,0) is an analytic map germ such that and f satisfies a certain non-degeneracy condition with respect to a Newton polyhedron Γ₊ ⊆ ℝⁿ, then the index of f only depends on the principal parts of f with respect to the compact faces of Γ₊. In particular, we obtain a known result on the index of semi-weighted-homogeneous map germs. We also discuss non-degenerate vector fields in the sense of Khovanskiĭand special applications of our results to planar analytic vector fields....
The infinitesimal M. Noether theorem for singularities
The Infinitesimal Torelli Problem for Zero Sets of Sections of Vector Bundles.
The inner Carathédory distance for the annulus.
The interpolation theorem for holomorphic generalized functions
The Intersection Matrix of Brieskorn Singularities.
The Intersection of the Closures of Two Disjoint Strongly Pseudoconvex Domains.
The invariant holonomic system on a semisimple Lie algebra.
The Iversen theorem in a polydisc.
The Jacobian conjecture and the extensions of polynomial embeddings.
The Jacobian Conjecture: survey of some results
The paper contains the formulation of the problem and an almost up-to-date survey of some results in the area.
The jump of the Milnor number in the X 9 singularity class
The jump of the Milnor number of an isolated singularity f 0 is the minimal non-zero difference between the Milnor numbers of f 0 and one of its deformations (f s). We prove that for the singularities in the X 9 singularity class their jumps are equal to 2.