Now showing items 1-20 of 32

    • Equisingularity in One-Parameter Families of Generically Reduced Curves 

      Fernández de Bobadilla J.; Snoussi J.; Spivakovsky M. (International Mathematics Research Notices, 2016-01-01)
      We explore some equisingularity criteria in one-parameter families of generically reduced curves. We prove the equivalence between Whitney regularity and Zariski’s discriminant criterion. We prove that topological triviality ...
    • A Short Survey on the Integral Identity Conjectureand Theories of Motivic Integration 

      Thuong L.Q. (Acta Mathematica Vietnamica, 2016-12-16)
      In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ...
    • 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\, ...
    • Singularities of the Hilbert scheme of effective divisors 

      Dan A. (2017-01-10)
      In this article, we study the Hilbert scheme of effective divisors in smooth hypersurfaces in $\mathbb{P}^3$, a topic not extensively studied. We prove that there exists such effective divisors $D$ satisfying the property: ...
    • A specialization property of index 

      Dan A.; Kaur I. (2017-01-10)
      In [Kol13] Kollár defined $i$-th index of a proper scheme over a field. In this note we study how index behaves under specialization, in any characteristic.
    • 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 ...
    • 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)
      [TBA]
    • Surgery formulae for the Seiberg-Witten invariant of plumbed 3-manifolds 

      László T.; Nagy J.; Némethi A. (2017-02)
      Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3--manifold associated with a connected negative definite graph $\mathcal{T}$. We consider the combinatorial multivariable Poincar\'e series associated ...
    • Criterion for logarithmic connections with prescribed residues 

      Biswas I.; Dan A.; Paul A. (Manucripta Mathematica, 2017-04-01)
      A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset ...
    • A Short Survey on the Integral Identity Conjecture and Theories of Motivic Integration 

      Thuong L.Q. (Acta Mathematica Vietnamica, 2017-04-04)
      In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ...
    • Euler reflexion formulas for motivic multiple zeta functions 

      Thuong L.Q.; Nguyen H.D. (Journal of Algebraic Geometry, 2017-05-14)
      We introduce a new notion of $\boxast$-product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability of and commuting with the limit of rational ...
    • 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 ...
    • 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 ...
    • Representation of surface homeomorphisms by tête-à-tête graphs 

      Fernández de Bobadilla J.; Pe Pereira M.; Portilla Cuadrado P. (2017-06-21)
      We use tête-à-tête graphs as defined by N. A'campo and extended versions to codify all periodic mapping classes of an orientable surface with non-empty boundary, improving work of N. A'Campo and C. Graf. We also introduce ...
    • Right unimodal and bimodal singularities in positive characteristic 

      Nguyen H.D. (International Mathematics Research Notices, 2017-08-07)
      The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple ...
    • A proof of the integral identity conjecture, II 

      Thuong L.Q. (Comptes Rendus Mathematique, 2017-10-31)
      In this note, using Cluckers-Loeser’s theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.
    • Topology of Spaces of Valuations and Geometry of Singularities 

      de Felipe Ana B. (Transactions of the AMS - American Mathematical Society, 2017-11-11)
      Given an algebraic variety X defined over an algebraically closed field, we study the space RZ(X,x) consisting of all the valuations of the function field of X which are centered in a closed point x of X. We concentrate ...
    • 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 ...
    • 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 ...
    • 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 ...