Related papers: Integrable deformations of local analytic fibratio…

We prove the existence (and give a characterization) of a germ of complex analytic set left invariant by an abelian group of germs of holomorphic diffeomorphisms at a common fixed point.We also give condition that ensure that such a group…

We study the regularity of exceptional actions of groups by $C^{1,\alpha}$ diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first derivatives that are continuous with concave modulus of…

We introduce the concept of topological finite-determinacy for germs of analytic functions within a fixed ideal $I$, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We prove the…

We prove that a (branched) minimal immersion from $\mathbb{C}$ to $\mathbb{R}^n$ is stable if and only if it lives in an even dimensional affine subspace and is holomorphic for some orthogonal complex structure on the subspace. More…

We establish an integration theory for singular subalgebroids, by diffeological groupoids. To do so, we single out a class of diffeological groupoids satisfying specific properties, and we introduce a differentiation-integration procedure…

We consider germs of holomorphic vector fields at the origin of $\mathbb{C}^3$, with non-isolated singularities that are tangent to a holomorphic foliation of codimension one. This configuration is known as a $2$-flag of foliations. The…

Let f be a hypersurface surface local singularity whose zero set has 1-dimensional singular locus. We develop an explicit procedure that provides the boundary of the Milnor fibre of f as an oriented plumbed 3-manifold. The method provides…

Consider a singular holomorphic map-germ $f: (X,\underline{0}) \to (\mathbb C,0)$ where $X$ is a singular complex analytic variety in $\mathbb C^N$, and another holomorphic map-germ $g: (X,\underline{0}) \to (\mathbb C,0)$ which is…

We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of…

Let f and g be holomorphic function-germs vanishing at the origin of a complex analytic germ of dimension three. Suppose that they have no common irreducible component and that the real analytic map-germ given by the multiplication of f by…

We study the nilpotent part $N'$ of a pseudo-periodic automorphism $h$ of a real oriented surface with boundary $\Sigma$. We associate a quadratic form $Q$ defined on the first homology group (relative to the boundary) of the surface…

We study codimension one (transversally oriented) foliations $\fa$ on oriented closed manifolds $M$ having non-empty compact singular set $\sing(\fa)$ which is locally defined by Bott-Morse functions. We prove that if the transverse type of…

We study a germ of real analytic $n$-dimensional submanifold of ${\mathbf C}^n$ that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the maximum number of deck…

We prove stochastic homogenization for integral functionals defined on Sobolev spaces, where the stationary, ergodic integrand satisfies a degenerate growth condition of the form \begin{equation*} c|\xi A(\omega,x)|^p\leq…

We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension 1 (i.e. a double fixed point) under conjugacy. These generic unfolding depend on one real parameter. The classification is done…

Let $f$ be a Morse function on a closed surface $\Sigma$ such that zero is a regular value and such that $f$ admits neither positive minima nor negative maxima. In this expository note, we show that $\Sigma\times \mathbb{R}$ admits an…

Let $f:\mathbb{C}^{n+1} \to \mathbb{C}$ be a germ of hypersurface with isolated singularity. One can associate to $f$ a polarized variation of mixed Hodge structure $\mathcal{H}$ over the punctured disc, where the Hodge filtration is the…

Let F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the DG-Lie algebra RHom(F,F) of derived endomorphisms of F is formal. The proof is based on the study of equivariant $L_{\infty}$ minimal models…

Let $X$ be a germ of holomorphic vector field at the origin of ${\bf C}^n$ and vanishing there. We assume that $X$ is a "nondegenerate" good perturbation of a singular completely integrable system. The latter is associated to a family of…

We study under the standpoint of integrable complex analytic 1-forms (complex analytic foliations), a class of second order ordinary differential equations with periodic coefficients. More precisely, we study Hill's equations of motion of…