Now showing items 6-25 of 39

    • General tête-à-tête graphs and Seifert manifolds 

      Portilla Cuadrado P. (2018-02-10)
      Tête-à-tête graphs and relative tête-à-tête graphs were introduced by N. A’Campo in 2010 to model monodromies of isolated plane curves. By recent work of Fdez de Bobadilla, Pe Pereira and the author, they provide a way ...
    • Homogeneous singularity and the Alexander polynomial of a projective plane curve 

      Thuong L.Q.; Tai P.D.; Hoang Lan N.P. (2017-12-10)
      The Alexander polynomial of a plane curve is an important invariant in global theories on curves. However, it seems that this invariant and even a much stronger one the fundamental group of the complement of a plane curve ...
    • 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 ...
    • A Jacobian module for disentanglements and applications to Mond's conjecture 

      Fernández de Bobadilla J.; Nuño-Ballesteros J.J.; Peñafort-Sanchis G. (2017-01-10)
    • 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 $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, ...
    • 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 ...
    • Logarithmic connections on principal bundles over a Riemann surface 

      Biswas I.; Dan A.; Paul A.; Saha A. (arxiv, 2017)
      Let $E_G$ be a holomorphic principal $G$--bundle on a compact connected Riemann surface $X$, where $G$ is a connected reductive complex affine algebraic group. Fix a finite subset $D\, \subset\, X$, and for each $x\,\in\, ...
    • 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 ...
    • Monodromies as tête-à-tête graphs 

      Portilla Cuadrado P. (2018-05-08)
    • 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 ...
    • 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- ...
    • 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 ...
    • Non-normal affine monoids, modules and Poincaré series of plumbed 3-manifolds 

      László T.; Szilágyi Zs. (Acta Mathematica Hungarica, 2017-05-18)
      We construct a non-normal affine monoid together with its modules associated with a negative definite plumbed 3-manifold M. In terms of their structure, we describe the $H_1(M,\mathbb{Z})$-equivariant parts of the topological ...
    • A note on the determinant map 

      Dan A.; Kaur I. (2017-01-10)
      Classically, there exists a determinant map from the moduli space of semi-stable sheaves on a smooth, projective variety to the Picard scheme. Unfortunately, if the underlying variety is singular, then such a map does not ...
    • On intersection cohomology with torus actions of complexity one 

      Agustín M.; Langlois K. (Revista Matemática Completense, 2017-05-20)
      The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given an algebraic torus T, one of our result determines the intersection cohomology Betti numbers of ...
    • On Lipschitz rigidity of complex analytic sets 

      Fernandes A.; Sampaio J. E. (The Journal of Geometric Analysis, 2019-02-26)
      We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of ...
    • On the generalized Nash problem for smooth germs and adjacencies of curve singularities 

      Fernández de Bobadilla J.; Pe Pereira M.; Popescu-Pampu P. (Advances in Mathematics, 2017-12-10)
      In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine whether the arc space of one of them is included in the arc space ...
    • 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 ...
    • 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, ...