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On the versal discriminant of J k , 0 singularities

Piotr Jaworski (1996)

Annales Polonici Mathematici

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 to analytic triviality of an unfolding or deformation along the moduli. The versal discriminant of the Pham singularity ( J 3 , 0 in Arnold’s classification) was thoroughly investigated by J. Damon and A. Galligo [2], [3], [4]. The goal of this paper is to continue their work and...

On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold

Zhiwei Wang (2016)

Annales Polonici Mathematici

This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that ∂ ∂ ̅ ω k = 0 for all k, we generalize the volume of the cohomology class in the Kähler setting to the Hermitian setting, and prove that the volume is always finite and the Grauert-Riemenschneider type criterion holds true, which is a partial answer to a conjecture posed by Boucksom. Secondly, we observe that if the anticanonical bundle K X - 1 is nef, then for any ε >...

On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball

Nikolai Nikolov, Pascal J. Thomas (2008)

Annales Polonici Mathematici

Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a “generalized” tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone C A to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.

On topological classification of complex mappings

Hadi Seyedinejad, Ali Zaghian (2015)

Annales Polonici Mathematici

We study the topological invariant ϕ of Kwieciński and Tworzewski, particularly beyond the case of mappings with smooth targets. We derive a lower bound for ϕ of a general mapping, which is similarly effective as the upper bound given by Kwieciński and Tworzewski. Some classes of mappings are identified for which the exact value of ϕ can be computed. Also, we prove that the variation of ϕ on the source space of a mapping with a smooth target is semicontinuous in the Zariski topology.

On transcendental automorphisms of algebraic foliations

B. Scárdua (2003)

Fundamenta Mathematicae

We study the group Aut(ℱ) of (self) isomorphisms of a holomorphic foliation ℱ with singularities on a complex manifold. We prove, for instance, that for a polynomial foliation on ℂ² this group consists of algebraic elements provided that the line at infinity ℂP(2)∖ℂ² is not invariant under the foliation. If in addition ℱ is of general type (cf. [20]) then Aut(ℱ) is finite. For a foliation with hyperbolic singularities at infinity, if there is a transcendental automorphism then the foliation is either...

On unique range sets of meromorphic functions in ℂ m

Xiao-Tian Bai, Qi Han (2007)

Archivum Mathematicum

By considering a question proposed by F. Gross concerning unique range sets of entire functions in ℂ , we study the unicity of meromorphic functions in ℂ m that share three distinct finite sets CM and obtain some results which reduce 5 ≤ c 3 ( ℳ ( ℂ m ) ) ≤ 9 to 5 ≤ c 3 ( ℳ ( ℂ m ) ) ≤ 6 .

On vanishing inflection points of plane curves

Mauricio Garay (2002)

Annales de l’institut Fourier

We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs f : ( ℂ 2 , 0 ) ⟶ ( ℂ , 0 ) which take into account the inflection points of the fibres of f . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.

On vector fields in C3 without a separatrix.

J. Olivares-Vázquez (1992)

Revista Matemática de la Universidad Complutense de Madrid

A family of germs at 0 of holomorphic vector fields in C3 without separatrices is constructed, with the aid of the blown-up foliation F in the blown-up manifold C3. We impose conditions on the multiplicity and the linear part of F at its singular points (i.e., non-semisimplicity and certain nonresonancy), which are sufficient for the original vector field to be separatrix-free.

Currently displaying 561 – 580 of 607