相关论文: Weighted homogeneous singularities and rational ho…

In this paper, we propose an improved singularity structure simplification method for hexahedral (hex) meshes using a weighted ranking approach. In previous work, the selection of to-be-collapsed base complex sheets/chords is only based on…

We characterize sandwiched singularities in terms of their link in two different settings. We first prove that such singularities are precisely the normal surface singularities having self-similar non-archimedean links. We describe this…

Given a link of a normal surface singularity with its canonical contact structure, we compare the collection of its Stein fillings to its Milnor fillings (that is, Milnor fibers of possible smoothings). We prove that, unlike Stein fillings,…

For an isolated hypersurface singularity $f=0$, the Milnor number $\mu$ is greater than or equal to the Tjurina number $\tau$ (the dimension of the base of the semi-universal deformation), with equality if $f$ is quasi-homogeneous. K. Saito…

We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of a smoothing. Applications are given to several types of…

Let $X$ a complex projective variety of complex dimension $n$ with only isolated singularities of simply connected links. We show that we can endow the rational cohomology of the family of the $\overline{p}$-perverse intersection spaces $\{…

Let X be an affine normal variety with a C^*-action having only positive weights. Assume that X_{reg} has a symplectic 2-form w of weight l. We prove that, when l is not zero, the w is a unique symplectic 2-form of weight l up to…

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…

The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method of homology groups, namely the non-triviality of some…

For a weighted quasihomogeneous two dimensional hypersurface singularity, we define a smoothing with unipotent monodromy and an isolated graded normal singularity. We study the natural weighted blow up of both the smoothing and the surface.…

Using the picture deformation technique of De Jong-Van Straten we show that no singularity whose resolution graph has 3 or 4 large nodes, i.e., nodes satisfying d(v)+e(v)\leq -2, has a QHD smoothing. This is achieved by providing a general…

Given a canonically oriented Brieskorn sphere $Y=\Sigma(a_1,...,a_n)$, we confirm some statements conjectured by Gompf. More specifically, we obstruct the existence of rational homology ball symplectic fillings for any contact structure on…

Rationally null-homologous links in Seifert fibered spaces may be represented combinatorially via labeled diagrams. We introduce an additional condition on a labeled link diagram and prove that it is equivalent to the existence of a…

While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic hypersurfaces with an isolated singularity,…

We show that if a compact complex surface admits a locally conformally flat metric, then it cannot contain a smooth rational curve of odd self-intersection. In particular, the surface has to be minimal. Then we give a list of possibilities…

We study analytically the spacelike singularity inside a spherically-symmetric, charged black hole coupled to a self-gravitating spherical massless scalar field. We assume spatial homogeneity, and find a generic solution in terms of a…

We show that for every $\epsilon>0$, there exists a compact lamination by $\epsilon$-holomorphic surfaces in the complex projective plane, minimal, and that carries hyperbolic holonomy. We call $\epsilon$-holomorphic a real 2-dimensional…

Disk contact representations realize graphs by mapping vertices bijectively to interior-disjoint disks in the plane such that two disks touch each other if and only if the corresponding vertices are adjacent in the graph. Deciding whether a…

In this note we prove that, for any integer n, there exist a smooth 4-manifold, homotopic to a K3 surface, defined by applying the link surgery method of Fintushel-Stern to a certain 2-component graph link, which admits n inequivalent…

The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…