Now showing items 24-43 of 70

    • A Lê-Greuel type formula for the image Milnor number 

      Nuño-Ballesteros, J.J.; Pallarés Torres, I.Autoridad BCAM (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 ...
    • Linearization of holomorphic families of algebraic automor- phisms of the affine plane 

      Kuroda, S.; Kutzschebauch, F.; Pelka, T.R.Autoridad BCAM (2022-01-03)
      Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $\mathbb{C}^2$, holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular ...
    • Local Topological Obstruction For Divisors 

      Biswas, I.; Dan, A. (2020)
      Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is well-known that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in ...
    • Logarithmic connections on principal bundles over a Riemann surface 

      Biswas, I.; Dan, A.; Paul, A.; Saha, A. (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\, ...
    • Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature 

      Jeffries, J.; Nakajima, Y.; Smirnov, I.; Watanabe, K.; Yoshida, K. (2022)
      ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...
    • 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 ...
    • Moderately Discontinuous Algebraic Topology for Metric Subanalytic Germs 

      Heinze, S. (2019-10-31)
      We have developed both a homology theory and a homotopy theory in the context of metric subanalytic germs (see Definition 2.1). The former is called MD homology and is covered in Chapter 2, which contains a paper that is ...
    • Moderately Discontinuous Homology 

      Fernández de Bobadilla, J.Autoridad BCAM; Heinze, S.; Sampaio, J.E. (2021-01-01)
      We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of metric singular subanalytic germs. The main novelty of our approach is to allow ...
    • 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.Autoridad BCAM; Sampaio, J.E. (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 ...
    • Multiplicity of singularities is not a bi-Lipschitz invariant 

      Birbrair, L.; Fernandes, A.; Sampaio, J.E.; Verbitsky, M. (2020-01-17)
      It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.
    • Multiplicity, regularity and blow-spherical equivalence of complex analytic sets 

      Sampaio, J.E. (2020-01-29)
      This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blow-spherical equivalence and we obtain several applications with this new ...
    • The Nash Problem from a Geometric and Topological Perspective 

      Fernández de Bobadilla, J.Autoridad BCAM; 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- ...
    • The Nash Problem from Geometric and Topological Perspective 

      Fernández de Bobadilla, J.Autoridad BCAM; Pe Pereira, M. (2020-03-01)
      We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional ...
    • Némethi’s division algorithm for zeta-functions of plumbed 3-manifolds 

      László, T.; Szilágyi, Zs. (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 ...
    • Neron models of intermediate Jacobians associated to moduli spaces 

      Dan, A.; Kaur, I. (2019-12-01)
      Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projective curves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$ with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$ ...
    • Non-normal affine monoids, modules and Poincaré series of plumbed 3-manifolds 

      László, T.; Szilágyi, Zs. (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 a conjecture of harris 

      Dan, A. (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 ...
    • On intersection cohomology with torus actions of complexity one 

      Agustín, M.; Langlois, K. (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 ...