Taut Two-Dimensional Singularities.
The dynamics of holomorphic maps near curves of fixed points
Let be a two-dimensional complex manifold and a holomorphic map. Let be a curve made of fixed points of , i.e. . We study the dynamics near in case acts as the identity on the normal bundle of the regular part of . Besides results of local nature, we prove that if is a globally and locally irreducible compact curve such that then there exists a point and a holomorphic -invariant curve with on the boundary which is attracted by under the action of . These results are achieved...
The Hilbert modular group, resolution of the singularities at the cusps and related problems
The Milnor Number and Deformations of Complex Curve Singularities.
The Seiberg–Witten invariants of negative definite plumbed 3-manifolds
Assume that is a connected negative definite plumbing graph, and that the associated plumbed 3-manifold is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg–Witten invariant of . The first one is the constant term of a ‘multivariable Hilbert polynomial’, it reflects in a conceptual way the structure of the graph , and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second...
The Signature of Smoothings of Complex Surface Singularities.
Théorèmes de finitude en géométrie analytique
Topologie comparée d'une courbe polaire et de sa courbe descriminante.
Let f be an analytic function germ at 0 in C2. We compare the topological complexity of the discriminant curve of f to the one of its polar curve.
Topologie d'un polynôme de deux variables complexes au voisinage de l'infini
Nous donnons un système complet d’invariants de la classe de conjugaison topologique de polynômes de 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...
Toric embedded resolutions of quasi-ordinary hypersurface singularities
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...
Two Theorems on Higher Dimensional Singularities.
Two Theorems on Modifications of Analytic Spaces.