Now showing items 21-40 of 57

    • Mixed tête-à-tête twists as monodromies associated with holomorphic function germs 

      Portilla Cuadrado P.; Sigurdsson B. (2018-04-01)
      Tête-à-tête graphs were introduced by N. A’Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed tête-à-tête graphs provide a generalization which define mixed tête-à-tête twists, which ...
    • The Nash Problem from a Geometric and Topological Perspective 

      Fernández de Bobadilla J.; Pe Pereira M. (2018-04-17)
      We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the au- thors influenced it. Later we summarize the main ideas in the higher dimen- ...
    • A proof of the differentiable invariance of the multiplicity using spherical blowing-up 

      Sampaio J. E. (Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018-04-21)
      In this paper we use some properties of spherical blowing-up to give an alternative and more geometric proof of Gau-Lipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, ...
    • Monodromies as tête-à-tête graphs 

      Portilla Cuadrado P. (2018-05-08)
    • Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds 

      László T.; Nagy J.; Némethi A. (2018-06)
      Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the ‘periodic constant’ of the topological multivariable Poincaré series (zeta ...
    • Singularities in Geometry and Topology 

      Romano A. (2018-06-18)
      This thesis consists of two different topics that are not related. The thesis has two different and independent parts that can be read in any order. The purpose of this work is to study two topics in singularity theory: ...
    • Semialgebraic CMC surfaces in $\mathbb{R}^3$ with singularities 

      Sampaio J. E. (2018-06-30)
      In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we ...
    • Hölder equivalence of complex analytic curve singularities 

      Fernandes A.; Sampaio J. E.; Silva J. P. (Bulletin of the London Mathematical Society, 2018-08-06)
      We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$-H\"older ...
    • On Zariski’s multiplicity problem at infinity 

      Sampaio J. E. (Proceedings of the American Mathematical Society, 2018-08-14)
      We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must have the same degree. More specifically, ...
    • Some classes of homeomorphisms that preserve multiplicity and tangent cones 

      Sampaio J. E. (2018-08-19)
      In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ...
    • Némethi’s division algorithm for zeta-functions of plumbed 3-manifolds 

      László T.; Szilágyi Zs. (Bulletin of the London Mathematical Society, 2018-08-27)
      A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbing 3-manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta-function ...
    • Multiplicity and degree as bi‐Lipschitz invariants for complex sets 

      Fernandes A.; Fernández de Bobadilla J.; Sampaio J. E. (Journal of Topology, 2018-08-29)
      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 ...
    • On the geometry of strongly flat semigroups and their generalizations 

      László T.; Némethi A. (2018-09-18)
      Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and ...
    • A jacobian module for disentanglements and applications to Mond's conjecture 

      Fernández de Bobadilla J.; Nuño-Ballesteros J.J.; Peñafort-Sanchis G. (Revista Matemática Complutense, 2019)
      Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$-module $M(g)$ with the property that $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, ...
    • The Abel map for surface singularities I. Generalities and examples 

      Némethi A.; Nagy J. (Mathematische Annalen, 2019)
      Abstract. Let (X, o) be a complex normal surface singularity. We fix one of its good resolutions X → X, an effective cycle Z supported on the reduced exceptional curve, and any possible (first Chern) class l′ ∈ H 2 (X , ...
    • On the length of perverse sheaves on hyperplane arrangements 

      Budur N.; Liu Y. (european Journal of Mathematics, 2019)
      Abstract. In this article we address the length of perverse sheaves arising as direct images of rank one local systems on complements of hyperplane arrangements. In the case of a cone over an essential line arrangement ...
    • On a conjecture of harris 

      Dan A. (World Scientific, 2019)
      For d ≥ 4, the Noether-Lefschetz locus NLd parametrizes smooth, degree d sur- faces in P3 with Picard number at least 2. A conjecture of Harris states that there are only finitely many irreducible components of the ...
    • The abel map for surface singularities II. Generic analytic structure 

      Nagy J.; Nemethi A. (Advances in Mathematics, 2019)
      We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure ...
    • A Lê-Greuel type formula for the image Milnor number 

      Nuño-Ballesteros J.J.; Pallarés Torres I. (Hokkaido Mathematical Journal, 2019-02)
      Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n-1},0)\to ...