Fortsetzungsdefekte zweidimensionaler abelscher Quotienten-Singularitäten.
Frobenius avec singularites. 2. Le cas general
Frobenius avec singularités. I. Codimension un
Fronces et doubles plis
Front d'onde et propagation des singularités pour un vecteur-distribution
We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.
Frontière d'une hypersurface pfaffienne
Function germs defined on isolated hypersurface singularities
Gauss-Manin connections of Schläfli type for hypersphere arrangements
The cohomological structure of hypersphere arragnements is given. The Gauss-Manin connections for related hypergeometrtic integrals are given in terms of invariant forms. They are used to get the explicit differential formula for the volume of a simplex whose faces are hyperspheres.
Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)
We associate to any convenient nondegenerate Laurent polynomial on the complex torus a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of (or its universal unfolding) and of the corresponding Hodge theory.
Generalised Magnus modules over the braid group.
Generalized local and global Sebastiani-Thom type theorems
Generalized transversely projective structure on a transversely holomorphic foliation.
Germs of holomorphic vector fields in C3 without a separatrix.
Gluing Cohen-Macaulay modules with applications to quasihomogeneous complete intersections with isolated singularities.
Graph theoretic techniques in algebraic geometry II: construction of singular complex surfaces of the rational cohomology type of CP2.
Gromov–Witten invariants for mirror orbifolds of simple elliptic singularities
We consider a mirror symmetry of simple elliptic singularities. In particular, we construct isomorphisms of Frobenius manifolds among the one from the Gromov–Witten theory of a weighted projective line, the one from the theory of primitive forms for a universal unfolding of a simple elliptic singularity and the one from the invariant theory for an elliptic Weyl group. As a consequence, we give a geometric interpretation of the Fourier coefficients of an eta product considered by K. Saito.
Groupe de monodromie géométrique des singularités simples.
Hamiltonian stability and subanalytic geometry
In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry, we derive a geometric criterion for steepness: a numerical function which is real analytic around a...
Harmonic metrics and connections with irregular singularities
We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface with the complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same complex.
Hermitian (a,b)-modules and Saito's "higher residue pairings"
Following the work of Daniel Barlet [Pitman Res. Notes Math. Ser. 366 (1997), 19-59] and Ridha Belgrade [J. Algebra 245 (2001), 193-224], the aim of this article is to study the existence of (a,b)-hermitian forms on regular (a,b)-modules. We show that every regular (a,b)-module E with a non-degenerate bilinear form can be written in a unique way as a direct sum of (a,b)-modules that admit either an (a,b)-hermitian or an (a,b)-anti-hermitian form or both; all three cases are possible, and we give...