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Artículo
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Specializations of MacMahon symmetric functions and the polynomial algebra
(Elsevier, 2002-03-06)
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. We use a combinatorial construction of the different bases of the ...
Artículo
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Exponents of Some One-Dimensional Gauss–Manin Systems
(European Mathematical Society Publishing House, 2017-07-03)
In this paper we provide a purely algebraic characterization of the exponents of one-dimensional direct images of a structure sheaf by a rational function, related to the vanishing of the cohomologies of a certain Koszul ...
Tesis Doctoral
Artículo
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Rectangular symmetries for coe cients of symmetric functions
(The Electronic Journal of Combinatorics, 2015-07-31)
We show that some of the main structural constants for symmetric functions (Littlewood-Richardson coe cients, Kronecker coe cients, plethysm coe cients, and the Kostka{Foulkes polynomials) share symmetries related to the ...
Tesis Doctoral
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Soluciones Gevrey de sistemas hipergeométricos
(2010)
Esta memoria versa sobre la irregularidad de los D-módulos hipergeométricos MA(β)(cf. Definición 3.1.3), introducidos p or Gelfand, Graev, Kapranov y Zelevinsky [GGZ87], [GZK89]. Nuestro estudio se basa principalmente en ...
Artículo
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Dualité et comparaison sur les complexes de de Rham logarithmiques par rapport aux diviseurs libres
(Association des Annales de l'Institut Fourier, 2005)
Let X be a complex analytic manifold and D \subset X a free divisor. Integrable logarithmic connections along D can be seen as locally free {\cal O}_X-modules endowed with a (left) module structure over the ring of logarithmic ...
Artículo
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Rings of differential operators as enveloping algebras of Hasse–Schmidt derivations
(Elsevier, 2020-01)
Let k be a commutative ring and A a commutative k-algebra. In this paper we introduce the notion of enveloping algebra of Hasse–Schmidt derivations of A over k and we prove that, under suitable smoothness hypotheses, the ...
Tesis Doctoral
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Ramificación de valoraciones de superficies algebroides
(1981)
Se construyen las valoraciones de un cuerpo de funciones heromorfas formales en dos variables y se estudia la ramificación de algunos tipos de ellas. Especial atención se dedica al estudio de las singularidades de superficies ...
Artículo
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Conservation of the noetherianity by perfect transcendental field extensions
(European Mathematical Society, 2003)
Let k be a perfect field of characteristic p>0, k(t)per the perfect closure of k(t) and A a k-algebra. We characterize whether the ring A⊗kk(t)per is noetherian when A is the ring of formal power series in n indeterminates over k.
Artículo
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Gröbner δ-bases and Gröbner bases for differential operators
(Polish Academy of Sciences, Institute of Mathematics, 2002)
This paper deals with the notion of Gr¨obner δ-base for some rings of linear differential operators by adapting the works of W. Trinks, A. Assi, M. Insa and F. Pauer. We compare this notion with the one of Gröbner base for ...