On the conflict variety of an isolated hypersurface singularity.
On the degree of C...-determinacy.
On the Determinacy of Smooth Map-Germs.
On the existence and stability of unfoldings of equivariant two-parameter bifurcation problems.
On the Hyperbolicity Domain of the Polynomial x^n + a1x^(n-1) + 1/4+ an
∗ Partially supported by INTAS grant 97-1644We consider the polynomial Pn = x^n + a1 x^(n−1) + · · · + an , ai ∈ R. We represent by figures the projections on Oa1 . . . ak , k ≤ 6, of its hyperbolicity domain Π = {a ∈ Rn | all roots of Pn are real}. The set Π and its projections Πk in the spaces Oa1 . . . ak , k ≤ n, have the structure of stratified manifolds, the strata being defined by the multiplicity vectors. It is known that for k > 2 every non-empty fibre of the projection Π^k → Π^(k−1) is...
On the local structure of a generic central set
On the mass spectrum of Higgs particles
On the minima of functionals with linear growth
On the Pham example and the universal topological stratification of singularities
On the structure of a Morse form foliation
The foliation of a Morse form on a closed manifold is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of and . Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of and . The set of the ranks of all forms defining a given foliation without minimal...
On the symmetry of Stokes regions of a simple singularity.
On Topological Stability of Divergent Diagrams of Folds.
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.
Overdetermined Strata in General Families of Polynomials
2000 Mathematics Subject Classification: 12D10.In the paper we give different examples of overdetermined strata.