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Topological triviality of versal unfoldings of complete intersections

James Damon (1984)

Annales de l'institut Fourier

We obtain algebraic and geometric conditions for the topological triviality of versal unfoldings of weighted homogeneous complete intersections along subspaces corresponding to deformations of maximal weight. These results are applied: to infinite families of surface singularities in C 4 which begin with the exceptional unimodular singularities, to the intersection of pairs of generic quadrics, and to certain curve singularities.The algebraic conditions are related to the operation of adjoining powers,...

Topologie des fonctions régulières et cycles évanescents.

Thomas Brélivet (2003)

Revista Matemática Complutense

One has two notions of vanishing cycles: the Deligne's general notion and a concrete one used recently in the study of polynomial functions. We compare these two notions which gives us in particular a relative connectivity result. We finish with an example of vanishing cycle calculation which shows the difficulty of a good choice of compactification.

Topologie d'un polynôme de deux variables complexes au voisinage de l'infini

Laurence Fourrier (1996)

Annales de l'institut Fourier

Nous donnons un système complet d’invariants de la classe de conjugaison topologique de polynômes de ℂ 2 en dehors d’un compact suffisamment grand dans les deux sens suivants : en tant que feuilletages (en oubliant les valeurs des fibres) et en tant que fonctions. Ces invariants sont donnés par un arbre pondéré, fléché et coloré, obtenu à partir de la résolution des singularités du polynôme sur la droite à l’infini. Nous donnons un critère de régularité pour les valeurs d’un polynôme et une description...

Topology and geometry of caustics in relation with experiments

Alain Joets (1999)

Banach Center Publications

Caustics of geometrical optics are understood as special types of Lagrangian singularities. In the compact case, they have remarkable topological properties, expressed in particular by the Chekanov relation. We show how this relation may be experimentally checked on an example of biperiodic caustics produced by the deflection of the light by a nematic liquid crystal layer. Moreover the physical laws may impose a geometrical constraint, when the system is invariant by some group of symmetries. We...

Topology of arrangements and position of singularities

Enrique Artal Bartolo (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees)...

Toric embedded resolutions of quasi-ordinary hypersurface singularities

Pedro D. González Pérez (2003)

Annales de l’institut Fourier

We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the singularity. This result answers an open problem of Lipman in Equisingularity and simultaneous resolution of singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485- 503. In the first procedure the singularity is...

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