Recent Submissions

  • Classification of Lipschitz simple function germs 

    Nguyen, N.; Ruas, M.; Trivedi, S. (2020-07-01)
    It was shown by Henry and Parusiński in 2003 that the bi-Lipschitz right equivalence of function germs admits moduli. In this article, we introduce the notion of Lipschitz simple function germ and present the complete ...
  • Image Milnor Number Formulas for Weighted-Homogeneous Map-Germs 

    Pallarés, Irma; Peñafort Sanchis, Guillermo (2021-07-05)
    We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely ...
  • Classification of smooth factorial affine surfaces of Kodaira dimension zero with trivial units 

    Pełka, T.; Raźny, P. (2021-07-31)
    We give a corrected statement of (Gurjar and Miyanishi 1988, Theorem 2), which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such ...
  • Some contributions to the theory of singularities and their characteristic classes 

    Pallarés Torres, I.Autoridad BCAM (2021-06-02)
    In this Ph.D. thesis, we give some contributions to the theory of singularities, as well as to the theory of characteristic classes of singular spaces. The first part of this thesis is devoted to the theory of singularities ...
  • Decomposition theorem and torus actions of complexity one 

    Agustin, M.; Langlois, K. (2020)
    We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one.
  • The abel map for surface singularities II. Generic analytic structure 

    Nagy, J.; Nemethi, A. (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 ...
  • Reflection maps 

    Peñafort, G. (2020)
    Given a reflection group G acting on a complex vector space V , a reflection map is the composition of an embedding X → V with the quotient map V → Cp of G. We show how these maps, which can highly singular, may be studied ...
  • 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 ...
  • Kato-matsumoto-type results for disentanglements 

    Peñafort, G.; Zach, M. (2020)
    We consider the possible disentanglements of holomorphic map germs f : (Cn, 0) → (CN , 0), 0 < n < N, with nonisolated locus of instability Inst(f). The aim is to achieve lower bounds for their (homological) connectiv- ity ...
  • 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 the length of perverse sheaves on hyperplane arrangements 

    Budur, N.Autoridad BCAM; Liu, Y. (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 ...
  • The Abel map for surface singularities I. Generalities and examples 

    Némethi, A.Autoridad BCAM; Nagy, J. (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 , ...
  • Some classes of homeomorphisms that preserve multiplicity and tangent cones 

    Sampaio, J.E. (2020-01-01)
    In this paper we present some applications of A’Campo-Lˆe’s Theorem and we study some relations between Zariski’s Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent ...
  • 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 ...
  • Equivariant motivic integration and proof of the integral identity conjecture for regular functions 

    Le, Q.; Nguyen, H.D. (2019-12-02)
    We develop Denef-Loeser’s motivic integration to an equivariant version and use it to prove the full integral identity conjecture for regular functions. In comparison with Hartmann’s work, the equivariant Grothendieck ...
  • Topological invariants of plane curve singularities: Polar quotients and Lojasiewicz gradient exponents 

    Nguyen, H.D.; Pham, T.-S.; Hoàng, P.-D (2019-10-21)
    In this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are not necessarily reduced. We first show that, for complex plane curve singularities, the set of polar quotients is a ...
  • Globally subanalytic CMC surfaces in $\mathbb{R}^3$ with singularities 

    Sampaio, J.E. (2020-03-02)
    In this paper we present a classification of a class of globally subanalytic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016. We show that a globally subanalytic ...
  • 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 ...
  • 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 $\mathcal{X}$ ...
  • 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.