Now showing items 1-12 of 12

    • Bernstein-Sato polynomial of plane curves and Yano's conjecture 

      Blanco Fernández, Guillem (Universitat Politècnica de Catalunya, 2020-04-16)
      Doctoral thesis
      Open Access
      The main aim of this thesis is the study of the Bernstein-Sato polynomial of plane curve singularities. In this context, we prove a conjecture posed by Yano about the generic b-exponents of a plane irreducible curve. In ...
    • Bernstein–Sato theory for determinantal ideals in positive characteristic 

      López Sancha, Pedro (Universitat Politècnica de Catalunya, 2023-05-24)
      Bachelor thesis
      Open Access
      Covenantee:   University of Utah
      Sigui R un anell de polinomis sobre un cos k. Una varietat algebraica sobre k és un conjunt de punts on s'anul·len alguns polinomis de R. Amb la finalitat d'estudiar aquestes varietats i les seves singularitats, una pràctica ...
    • Effective computation of base points of two-dimensional ideals 

      Blanco Fernández, Guillem (Universitat Politècnica de Catalunya, 2015-10)
      Master thesis
      Open Access
      This works focus on computational aspects of the theory of singularities of plane algebraic curves. We show how to use the Puiseux factorization of a curve, computed through the Newton-Puiseux algorithm, to study the ...
    • Extremal mixed graphs in the context of the Degree/Diameter problem 

      Monserrat Companys, Joaquim (Universitat Politècnica de Catalunya, 2016-10)
      Master thesis
      Restricted access - confidentiality agreement
      Covenantee:   Universitat de Lleida. Grup de recerca Criptografia i Grafs
    • Finiteness properties of local cohomology modules 

      Quingles Daví, Guillem (Universitat Politècnica de Catalunya, 2022-09)
      Master thesis
      Open Access
      Local cohomology modules are one of the central objects in commutative algebra. However, the structure of these modules is still full of mystery. Lyubeznik conjectured that the number of associated primes and all the Bass ...
    • Limit distribution of Hodge spectral exponents of plane curve singularities 

      Gómez López, Roger (Universitat Politècnica de Catalunya, 2023-09-14)
      Master thesis
      Open Access
      K. Saito va formular la pregunta de si una distribució continua és el límit de la distribució dels exponents espectrals de Hodge a l'interval [0,1) d'una hipersuperfície quan aquesta es mou en un sentit que s'ha de precisar. ...
    • Multiplier ideals in two-dimensional local rings with rational singularities 

      Dachs Cadefau, Ferran (Universitat Politècnica de Catalunya, 2016-06-13)
      Doctoral thesis
      Open Access
      Covenantee:   Katholieke Universiteit te Leuven
      The aim of this memoir is to study multiplier ideals in two-dimensional local rings having at worst rational singularities. We also want to extend this study to the case of mixed multiplier ideals. The main achievements ...
    • Multiplier ideals of plane curves 

      Dachs Cadefau, Ferran (Universitat Politècnica de Catalunya, 2012-10)
      Master thesis
      Restricted access - author's decision
      Multiplier ideals and their corresponding jumping numbers have been revealed as a fundamental tool to measure the singularity of plane curves. There are approaches to these objects from both Commutative Algebra and Algebraic ...
    • Rings of differential operators on singular varieties 

      Barbero Lucas, Beatriz (Universitat Politècnica de Catalunya, 2022-07)
      Master thesis
      Open Access
      This project will be centered in the study of rings of differential operators on singular varieties and the theory of D-modules. We will start with the ring of k-linear differential operators on a polynomial ring. We will ...
    • Scheme of pairs of matrices with vanishing commutator 

      Llopis Vidal, Bartomeu (Universitat Politècnica de Catalunya, 2019-05-27)
      Bachelor thesis
      Open Access
      Covenantee:   Katholieke Universiteit te Leuven
      Let $X$ be smooth projective curve of genus $g$. Let $R(g,n)$ be $Hom(\pi_1(X),GL_n(C)$ with the natural affine scheme structure. If $g>1$, it is known that the representation space $R(g,n)$ is an irreducible reduced normal ...
    • Singularities via the Frobenius homomorphism 

      Navarro Travesset, Oriol (Universitat Politècnica de Catalunya, 2022-10)
      Master thesis
      Open Access
      Resolution of singularities in algebraic varieties has been a topic of interest in commutative algebra and algebraic geometry during the last decades. Altough we have a theory of resolution of singularities for rings of ...
    • Study of roots of the Bernstein-Sato polynomial of plane curves 

      Gómez López, Roger (Universitat Politècnica de Catalunya, 2022-02)
      Bachelor thesis
      Open Access
      Covenantee:   Katholieke Universiteit te Leuven
      En aquest projecte estudiem les arrels del polinomi de Bernstein-Sato en el cas de singularitats de corbes planes. Les arrels del polinomi de Bernstein-Sato estan relacionades amb els pols de la funció zeta complexa a ...