On the Torsion of Brieskorn Modules of Homogeneous Polynomials
On the uniqueness of the quasihomogeneity
The aim of this paper is to show that the quasihomogeneity of a quasihomogeneous germ with an isolated singularity uniquely extends to the base of its analytic miniversal deformation.
On the vanishing of local homotopy groups for isolated singularities of complex spaces.
On the versal discriminant of singularities
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 ( 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 Versal Resolutions of Deformations of Rational Double Points.
On the volume of a pseudo-effective class and semi-positive properties of the Harder-Narasimhan filtration on a compact Hermitian manifold
This paper divides into two parts. Let (X,ω) be a compact Hermitian manifold. Firstly, if the Hermitian metric ω satisfies the assumption that 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 is nef, then for any ε >...
On the Zariski Tangent Space to a Complex Analytic Variety.
On topological classification of complex mappings
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 topological rigidity of projective foliations
On transcendental automorphisms of algebraic foliations
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 vanishing inflection points of plane curves
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 which take into account the inflection points of the fibres of . 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.
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.
Opérateurs différentiels sur les espaces analytiques.
Parabolic exhaustions and analytic coverings.
Partial resolutions of quotient singularities.
Period mapping via Brieskorn modules
Periodicity of Branched Cyclic Covers of Manifolds with Open Book Decomposition.
Perturbative expansions in quantum mechanics
We prove a analytic versal deformation theorem in the Heisenberg algebra. We define the spectrum of an element in the Heisenberg algebra. The quantised version of the Morse lemma already shows that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.
Perturbing plane cruve singularities.
We describe the singularity of all but finitely-many germs in a pencil generated by two germs of plane curve sharing no tangent.
Perverse sheaves with singularities along the curve Yn = Xm.