Related papers: On certain complex surface singularities

In this note we study several aspects of coisotropic submanifolds of a contact manifold. In particular we give a structure theorem for the singularity of the characteristic foliation of a coisotropic submanifold. Moreover we establish the…

We construct the analytic lattice cohomology associated with the analytic type of any complex normal surface singularity. It is the categorification of the geometric genus of the germ, whenever the link is a rational homology sphere. It is…

It is known that the lens space $L(2n,1)$ supports a virtually overtwisted contact structure arising as the boundary of the Milnor fiber of a complex hypersurface singularity. In this article we study the problem of realizing other…

We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two…

We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…

We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz homeomorphims at…

Let ${\mathcal Q}_n^d$ be the vector space of homogeneous forms of degree $d\ge 3$ on ${\mathbb C}^n$, with $n\ge 2$. The object of our study is the map $\Phi$, introduced in earlier articles by J. Alper, M. Eastwood and the author, that…

We propose a proof of the characterization of spherical hypersurfaces as the only strictly pseudoconvex hypersurfaces which have contracting germs of diffeomorphisms. Unlike previous proofs, our approach does not use Chern-Moser theory. It…

We study multi-parameters deformations of isolated singularity function-germs on either a subanalytic set or a complex analytic spaces. We prove that if such a deformation has no coalescing of singular points, then it has constant…

For a compact oriented smooth $n$-manifold $M$ and a codimension-$1$ homology class $\phi \in \operatorname{H}_{n-1}(M, \partial M)$, we investigate a simplicial complex $\mathcal{S}^\dagger(M, \phi)$ relating the properly embedded…

The main goal of this paper is the analytic classification of the germs of singular foliations generated, up to an analytic change of coordinates, by the germs of vector fields of form the…

We describe singularities of distance squared functions on singular surfaces in $\mathbb{R}^3$ parameterized by smooth map-germs $\mathcal{A}$-equivalent to one of $S_k$, $B_k$, $C_k$ and $F_4$ singularities in terms of extended geometric…

In this article, we consider a real smooth hypersurface $M\subset \mathbb C^2$, which is of infinite type at $p\in M$. The purpose of this paper is to show that the real vector space of tangential holomorphic vector field germs at $p$…

This paper is devoted to the study of the LNE property in complex analytic hypersurface parametrized germs, that is, the sets that are images of finite analytic map germs from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$. We prove that if…

We undertake a systematic study of Lipschitz Normally Embedded normal complex surface germs. We prove in particular that the topological type of such a germ determines the combinatorics of its minimal resolution which factors through the…

If all but two vertices of a triangulated sphere have degrees divisible by $k$, then the exceptional vertices are not adjacent. This theorem is proved for $k=2$ with the help of the coloring monodromy. For $k = 3, 4, 5$ colorings by the…

We give a classification of absolutely dicritical foliations of cusp type, that is, the germ of singularities of complex foliations in the complex plane topologically equivalent to the singularity given by the level of the meromorphic…

Following arXiv:2012.07351 [hep-th], we study quantum extremal surfaces in various families of cosmologies with Big-Crunch singularities, by extremizing the generalized entropy in 2-dimensional backgrounds which can be thought of as arising…

Let f be an isolated plane curve singularity with Milnor fiber of genus at least 5. For all such f, we give (a) an intrinsic description of the geometric monodromy group that does not invoke the notion of the versal deformation space, and…

We extend the circle of ideas from a previous paper on hypersurfaces to functions $f \colon (\mathbb C^n, 0) \to (\mathbb C^k, 0)$ with an isolated singularity in a stratified sense on an arbitrary, but fixed complex analytic germ $(X, 0)$.…