Artículos (Álgebra)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10804

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Matematicas experimentales
(Federación Española de Profesores de Matemáticas, 1992) Pérez Jiménez, Antonio de Jesús; Universidad de Sevilla. Departamento de álgebra
How to calculate the slopes of a D-module
(Foundation Compositio Mathematica, 1996) Assi, Abdallah; Castro Jiménez, Francisco Jesús; Granger, Michel; Universidad de Sevilla. Departamento de álgebra; Universidad de Sevilla. FQM333: Álgebra Computacional en Anillos no Conmutativos y Aplicaciones
Cohomology of the complement of a free divisor
(American Mathematical Society, 1996-08) Castro Jiménez, Francisco Jesús; Narváez Macarro, Luis; Mond, David; Universidad de Sevilla. Departamento de álgebra; Universidad de Sevilla. FQM333: Algebra Computacional en Anillos no Conmutativos y Aplicaciones
We prove that if D is a "strongly quasihomogeneous" free divi- sor in the Stein manifold X, and U is its complement, then the de Rham cohomology of U can be computed as the cohomology of the complex of mero- morphic differential forms on X with logarithmic poles along D, with exterior derivative. The class of strongly quasihomogeneous free divisors, introduced here, includes free hyperplane arrangements and the discriminants of stable mappings in Mather's nice dimensions (and in particular the discriminants of Coxeter groups).
Semblanza del profesor don Gonzalo Sánchez Vázquez
(Federación Española de Profesores de Matemáticas, 1997-06) Pérez Jiménez, Antonio de Jesús; Universidad de Sevilla. Departamento de álgebra
Combinatorics of syzygies for semigroup algebras
(Universitat de Barcelona, 1998) Briales Morales, Emilio; Pisón Casares, Pilar; Universidad de Sevilla. Departamento de álgebra; Dirección General de Investigación Científica y Técnica (DGICYT). España; Junta de Andalucía; Universidad de Sevilla. FQM-366 Álgebras de Semigrupos, Computación y Aplicaciones
We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.
Le théorème de continuité de la division dans les anneaux d'opérateurs différentiels
(De Gruyter, 1998) Mebkhout, Zoghman; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Dirección General de Investigación Científica y Técnica (DGICYT). España; Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
In this paper we prove the continuity of Weierstrass-Hironaka division of finite order linear differential operators over a complex analytic manifold X with respect to the induced topology by a canonical one of Fréchet nuclear on the sheaf script D∞X. As a consequence, admissible modules over script D∞X and coherent modules over script DX inherit a canonical locally convex structure and admit finite free resolutions with strict morphisms. This structure allows, as example, to give a topological caracterisation of regularity and to prove that the existence of a regular Bernstein-Sato functional equation for a coherent script DX-module, M, with respect to an arbitrary divisor Y ⊂ X, implies the comparison theorem script D∞X ⊗script DX M[*Y] ≃ j*j-1 M∞.
Logarithmic differential operators and logarithmic de Rham complexes relative to a free divisor
(Elsevier, 1999) Calderón Moreno, Francisco Javier; Universidad de Sevilla. Departamento de álgebra; Dirección General de Investigación Científica y Técnica (DGICYT). España; Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
We prove a structure theorem for differential operators in the 0-th term of the V-filtration relative to a free divisor. manifold. As an application, we give a formula for the logarithmic de Rham complex with respect to a free divisor in terms of V0-modules, which generalizes the classical formula for the usual de Rham complex in terms of D-modules, and the formula of Esnault-Viehweg in the case of a normal crossing divisor. We also give a sufficient algebraic condition for perversity of the logarithmic de Rham complex.
Cohomologie évanescente p-adique: calculs locaux
(Università di Padova, 2000) Gros, Michel; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Universidad de Sevilla. FQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades
The Gröbner fan of an An-module
(Elsevier, 2000-06-14) Assi, Abdallah; Castro Jiménez, Francisco Jesús; Granger, Michel; Universidad de Sevilla. Departamento de álgebra; Dirección General de Investigación Científica y Técnica (DGICYT). España; Universidad de Sevilla. FQM333: Álgebra Computacional en Anillos no Conmutativos y Aplicaciones
Let I be a non-zero left ideal of the Weyl algebra An of order n over a field k and let L:R2n→R be a linear form defined by L(α,β)=∑i=1neiαi+∑i=1nfiβi. If ei+fi≥0, then L defines a filtration F•L on An. Let grL(I) be the graded ideal associated with the filtration induced by F•L on I. Let finally U denote the set of all linear form L for which ei+fi≥0 for all 1≤i≤n. The aim of this paper is to study, by using the theory of Gröbner bases, the stability of grL(I) when L varies in U. In a previous paper, we obtained finiteness results for some particular linear forms (used in order to study the regularity of a D-module along a smooth hypersurface). Here we generalize these results by adapting the theory of Gröbner fan of Mora-Robbiano to the D-module case. Our main tool is the homogenization technique initiated in our previous paper, and recently clarified in a work by F. Castro-Jiménez and L. Narváez-Macarro.
Continuous division of differential operators
(Association des Annales de l'Institut Fourier, 2001) Hauser, Herwig; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Dirección General de Investigación Científica y Técnica (DGICYT). España; Dirección General de Enseñanza Superior. España; Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
In this paper, we give a new proof of the continuity of division by differential operators with analytic coefficients, originally proved by Mebkhout and the second author. Our methods come from the proof of the Constant Rank Theorem for analytic maps between power series spaces, given by Müller and the first author.
A computational approach to the D-module of meromorphic functions
(2001) Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María; Universidad de Sevilla. Departamento de álgebra
Let D be a divisor in Cn. We present methods to compare the D-module of the meromorphic functions O[∗D] to some natural approximations. We show how the analytic case can be treated with computations in the Weyl algebra.
New presentations of surface braid groups
(World Scientific Publishing, 2001) González-Meneses López, Juan; Universidad de Sevilla. Departamento de álgebra; Dirección General de Enseñanza Superior. España; Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
In this paper we give new presentations of the braid groups and the pure braid groups of a closed surface. We also give an algorithm to solve the word problem in these groups, using the given presentations.
The regularity of a toric variety
(Elsevier, 2001-03-01) Briales Morales, Emilio; Pisón Casares, Pilar; Universidad de Sevilla. Departamento de álgebra; Universidad de Sevilla. FQM-366 Álgebras de Semigrupos, Computación y Aplicaciones
We give a method for computing the degrees of the minimal syzygies of a toric variety by means of combinatorial techniques. Indeed, we complete the explicit description of the minimal free resolution of the associated semigroup algebra, using the simplicial representation of Koszul homology which appeared in A. Campillo and C. Marijuán (1991, Sém. Théor. Nombres Bordeaux3, 249–260). As an application, we obtain an algorithm for computing the Castelnuovo–Mumford regularity of a projective toric variety. This regularity is explicitly bounded by means of the semigroup generators which parametrize the variety.
El Año Mundial de las Matemáticas en Andalucía
(Federación Española de Profesores de Matemáticas, 2001-06) Pérez Jiménez, Antonio de Jesús; Universidad de Sevilla. Departamento de álgebra
On the dimension of discrete valuations of k ((X1, ..., Xn))
(Elsevier, 2001-07-01) Olalla Acosta, Miguel Ángel; Universidad de Sevilla. Departamento de álgebra; Junta de Andalucía; Universidad de Sevilla. FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
Let v be a rank-one discrete valuation of the field Kn=k((X1,…,Xn)). We know, after [1], that if n=2 then the dimension of v is 1 and if v is the usual order function over k((X1,…,Xn)) its dimension is n−1. In this paper we prove that, in the general case, the dimension of a rank-one discrete valuation can be any number between 1 and n−1.
The Kronecker product of Schur functions indexed by two-row shapes or hook shapes
(Springer, 2001-09) Rosas Celis, Mercedes Helena; Universidad de Sevilla. Departamento de álgebra
The Kronecker product of two Schur functions sµ and sν, denoted by sµ ∗ sν, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions µ and ν. The coefficient of sλ in this product is denoted by γ λ µν , and corresponds to the multiplicity of the irreducible character χ λ in χ µχ ν We use Sergeev’s Formula for a Schur function of a difference of two alphabets and the comultiplication expansion for sλ[XY ] to find closed formulas for the Kronecker coefficients γ λ µν when λ is an arbitrary shape and µ and ν are hook shapes or two-row shapes. Remmel [9 J.B. Remmel, “A formula for the Kronecker product of Schur functions of hook shapes,” J. Algebra 120, 1989, pp. 100–118, 10 J.B. Remmel, “Formulas for the expansion of the Kronecker products S(m,n) ⊗ S(1p−r,r) and S(1k2 l) ⊗ S(1p−r,r) ,” Discrete Math. 99, 1992, pp. 265–287] and Remmel and Whitehead [11] J.B. Remmel and T. Whitehead, “On the Kronecker product of Schur functions of two row shapes,” Bull. Belg. Math. Soc. Simon Stevin 1, 1994, pp. 649–683. derived some closed formulas for the Kronecker product of Schur functions indexed by two-row shapes or hook shapes using a different approach. We believe that the approach of this paper is more natural. The formulas obtained are simpler and reflect the symmetry of the Kronecker product.
The analytic standard fan of a D-module
(Elsevier, 2001-10-24) Assi, Abdallah; Castro Jiménez, Francisco Jesús; Granger, Michel; Universidad de Sevilla. Departamento de álgebra; Universidad de Sevilla. FQM333: Álgebra Computacional en Anillos no Conmutativos y Aplicaciones
We extend to the analytic D-module case our results in the algebraic case, namely, we associate with any monogeneous module over the ring D of germs of linear differential operators at the origin of Cn, with holomorphic coefficients, a combinatorial object which we call the standard fan of this D-module (see chapter 6 for a precise geometric description of this object). The main tool of the proof is the homogenization techniques and a convergent division theorem that we prove in the homogenization ring D[t].
MacMahon symmetric functions, the partition lattice, and young subgroups
(Elsevier, 2001-11) Rosas Celis, Mercedes Helena; Universidad de Sevilla. Departamento de álgebra; Universidad de Sevilla. FQM333: Algebra Computacional en Anillos no Conmutativos y Aplicaciones
A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we show that the MacMahon symmetric functions are the generating functions for the orbits of sets of functions indexed by partitions under the diagonal action of a Young subgroup of a symmetric group. We define a MacMahon chromatic symmetric function that generalizes Stanley's chromatic symmetric function. Then, we study some of the properties of this new function through its connection with the noncommutative chromatic symmetric function of Gebhard and Sagan.
Presentations for the monoids of singular braids on closed surfaces
(Taylor & Francis, 2002) González-Meneses López, Juan; Universidad de Sevilla. Departamento de álgebra; Dirección General de Enseñanza Superior e Investigación Científica (DGESIC). España; Universidad de Sevilla. FQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades
We give presentations, in terms of generators and relations, for the monoids SBn(M) of singular braids on closed surfaces. The proof of the validity of these presentations can also be applied to verify, in a new way, the presentations given by Birman for the monoids of Singular Artin braids.
Locally quasi-homogeneous free divisors are Koszul free
(MAIK Nauka/Interperiodica, 2002) Calderón Moreno, Francisco Javier; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de álgebra; Ministerio de Educación y Ciencia (MEC). España; Universidad de Sevilla. FQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades
Let X be a complex analytic manifold and D ⊂ X be a free divisor. If D is locally quasi-homogeneous, then the logarithmic de Rham complex associated to D is quasi-isomorphic to Rj∗(CX\D), which is a perverse sheaf. On the other hand, the logarithmic de Rham complex associated to a Koszul-free divisor is perverse. In this paper, we prove that every locally quasi-homogeneous free divisor is Koszul free.

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