The Intersection Matrix of Brieskorn Singularities.
The Lefshetz Vanishing Cycles on a Projective Nonsingular Plane Curve.
The Picard Group of a Quasi-Bundle.
The Shafarevich-Tate Conjecture for Pencils of Elliptic Curves on K3 Surfaces.
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...
The vanishing invariants in intersection homology of complex spaces
Théorèmes de Lefschetz en cohomologie cohérente et en cohomologie étale
Topologie des fonctions régulières et cycles évanescents.
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.
Topology of arrangements and position of singularities
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)...
Toroidal Degeneration of Abelian Varieties. II.
Towards a new interpretation of Milnor's number.
Travaux de Griffiths
Type III degenerations of K3 surfaces.