Tangent cones and Lipschitz stratifications
Taut, Pseudotaut and equisingularly rigid singularities.
Taut Two-Dimensional Singularities.
Techniques complexes d'étude d'E.D.O.
Tempered solutions of -modules on complex curves and formal invariants
Let be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of -modules on induces a fully faithful functor on a subcategory of germs of formal holonomic -modules. Further, given a germ of holonomic -module, we obtain some results linking the subanalytic sheaf of tempered solutions of and the classical formal and analytic invariants of .
The analytic Carathéodory conjecture.
The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
The asymptotic behavior of plurigenera for a normal isolated singularity.
The Bifurcation Set and Logarithmic Vector Fields.
The branching orders of a quasi-ordinary projection.
The characteristic variety of a generic foliation
We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.
The Complement of the Bifurcation Variety of a Simple Singularity
The ?-constant stratum is not smooth.
The differential Galois theory of regular singular p-adic differential equations.
The duals of generic hypersurfaces.
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 end curve theorem for normal complex surface singularities
We prove the “End Curve Theorem,” which states that a normal surface singularity with rational homology sphere link is a splice quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end curve function” is an analytic function whose zero set intersects in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf. A “splice quotient singularity” is described by giving an explicit set of equations describing...
The Euler number of the normalization of an algebraic threefold with ordinary singularities
By a classical formula due to Enriques, the Euler number χ(X) of the non-singular normalization X of an algebraic surface S with ordinary singularities in P³(ℂ) is given by χ(X) = n(n²-4n+6) - (3n-8)m + 3t - 2γ, where n is the degree of S, m the degree of the double curve (singular locus) of S, t is the cardinal number of the triple points of S, and γ the cardinal number of the cuspidal points of S. In this article we shall give a similar formula for an algebraic threefold with ordinary singularities...
The freeness of ideal subarrangements of Weyl arrangements
A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by Sommers–Tymoczko. In particular, when an ideal subarrangement is equal to the entireWeyl arrangement, our...
The geometric genus of hypersurface singularities
Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all superisolated and Newton non-degenerate hypersurface singularities.