Now showing items 1-20 of 22

    • A Koszul complex over skew polynomial rings 

      Álvarez Montaner, Josep; Boix, Alberto F.; Zarzuela Armengou, Santiago (2019-01-01)
      Article
      Open Access
      We construct a Koszul complex in the category of left skew polynomial rings associated with a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequence
    • An approach to the uniform Artin-Rees theorems from the notion of relation type 

      Planas Vilanova, Francesc d'Assís (2003)
      Article
      Open Access
    • Bernstein's inequality and holonomicity for certain singular rings 

      Álvarez Montaner, Josep; Jeffries, Jack; Núñez-Betancourt, Luis; Hernández, Daniel J.; Teixeira, Pedro; Witt, Emily E. (2021)
      Research report
      Open Access
      In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-modules for rings of invariants of finite groups in characteristic zero, and for strongly F-regular finitely generated graded ...
    • Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands 

      Álvarez Montaner, Josep; Jeffries, Jack; Núñez-Betancourt, Luis (2019)
      Research report
      Open Access
      This paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of ...
    • Bernstein-Sato polynomials in commutative algebra 

      Álvarez Montaner, Josep; Jeffries, Jack; Núñez-Betancourt, Luis (Springer Nature, 2022-02-23)
      Part of book or chapter of book
      Restricted access - publisher's policy
      This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra
    • 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 ...
    • D-modules, Bernstein-Sato polynomials and F-invariants of direct summands 

      Álvarez Montaner, Josep; Huneke, Craig; Núñez-Betancourt, Luis (2017-12-01)
      Article
      Open Access
      We study the structure of D -modules over a ring R which is a direct sum- mand of a polynomial or a power series ring S with coefficients over a field. We relate properties of D -modules over R to D -modules over S . We ...
    • Divisors of expected Jacobian type 

      Álvarez Montaner, Josep; Planas Vilanova, Francesc d'Assís (2021)
      Article
      Open Access
      Divisors whose Jacobian ideal is of linear type have received a lot of attention recently because of its connections with the theory of D-modules. In this work we are interested on divisors of expected Jacobian type, that ...
    • Emmy Noether i l’àlgebra commutativa 

      Zarzuela Armengou, Santiago (2009-02-18)
      Audiovisual
      Open Access
      Emmy Noether representa un punt d’inflexió fonamental en el desenvolupament de l’Àlgebra Commutativa. Per una banda, en ella conflueixen algunes de les línies evolutives prèvies més importants. Per altra, a partir del seu ...
    • 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 ...
    • Generating functions associated to Frobenius algebras 

      Álvarez Montaner, Josep (Elsevier, 2019-12-01)
      Article
      Open Access
      We introduce a generating function associated to the homogeneous gen-erators of a graded algebra that measures how far is this algebra from being finitelygenerated. For the case of some algebras of Frobenius endomorphisms ...
    • Hilbert Revisited 

      Buchsbaum, David (2009-03-18)
      Audiovisual
      Open Access
      Starting with a look at Hilbert's famous 1890 paper, which was considered at one time to have dealt the deathblow to Invariant Theory, and which inluded the famous Basis Theorem and Syzygy Theorem, we will trace some ...
    • Lyubeznik numbers of local rings and linear strands of graded ideals 

      Álvarez Montaner, Josep (Springer, 2016)
      Conference report
      Restricted access - publisher's policy
      We report recent work on the study of Lyubeznik numbers and their relation to invariants coming from the study of linear strands of free resolutions.
    • Lyubeznik numbers of local rings and linear strands of graded ideals 

      Álvarez Montaner, Josep (Springer, 2016)
      Part of book or chapter of book
      Restricted access - publisher's policy
      We report recent work on the study of Lyubeznik numbers and their relation to invariants coming from the study of linear strands of free resolutions
    • Minimal canonical comprehensive Gröbner systems 

      Manubens Ferriol, Montserrat; Montes Lozano, Antonio (2009)
      Article
      Open Access
      This is the continuation of Montes' paper "On the canonical discussion of polynomial systems with parameters''. In this paper, we define the Minimal Canonical Comprehensive Gröbner System of a parametric ideal and fix under ...
    • Minimal free resolutions of lattice ideals of digraphs 

      O'Carroll, Liam; Planas Vilanova, Francesc d'Assís (2018-03-02)
      Article
      Open Access
      Based upon a previous work of Manjunath and Sturmfels for a finite, complete, undirected graph, and a refined algorithm by Eröcal, Motsak, Schreyer and Steenpaß for computing syzygies, we display a free resolution of the ...
    • Monomial generators of complete planar ideals 

      Alberich Carramiñana, Maria; Álvarez Montaner, Josep; Blanco Fernández, Guillem (2020-01-01)
      Article
      Open Access
      We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements ...
    • On the integral degree of integral ring extensions 

      Giral Silió, José María; O'Carroll, Liam; Planas Vilanova, Francesc d'Assís; Plans Berenguer, Bernat (2019-02-01)
      Article
      Open Access
      Let A ¿ B be an integral ring extension of integral domains with fields of fractions K and L, respectively. The integral degree of A ¿ B, denoted by dA(B), is defined as the supremum of the degrees of minimal integral ...
    • Positivity properties of relative complete intersections 

      Barja Yáñez, Miguel Ángel; Stoppino, Lidia (2014-10)
      Research report
      Open Access
      We give conditions for f-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.
    • Rational parameterizations approach for solving equations in some dynamical systems problems 

      Lázaro Ochoa, José Tomás; Gasull Embid, Armengol; Torregrosa Arús, Joan (2019-08)
      Article
      Open Access
      We show how the use of rational parameterizations facilitates the study of the number of solutions of many systems of equations involving polynomials and square roots of polynomials. We illustrate the effectiveness of this ...