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Artículo
Gröbner bases and logarithmic D-modules
(Elsevier, 2006)
Let C[x] = C[x1, . . . , xn] be the ring of polynomials with complex coefficients and An the Weyl algebra of order n over C. Elements in An are linear differential operators with polynomial coefficients. For each polynomial ...
Artículo
On some D-modules in dimension 2
(Cornell University, 2000)
We prove a duality formula for two D-modules arising from logarithmic derivations w.r.t. a plane curve. As an application we give a differential proof of a logarithmic comparison theorem in [4].
Artículo
On the computation of Bernstein–Sato ideals
(Elsevier, 2004)
In this paper we compare the approach of Brianc¸onand Maisonobe for computing Bernstein–Sato ideals—based on computations in a Poincar´e–Birkhoff–Witt algebra—with the readily available method of Oaku and Takayama. We ...
Artículo
Logarithmic Comparison Theorem and some Euler homogeneous free divisors
(American Mathematical Society, 2005)
Let D, x be a free divisor germ in a complex manifold X of dimension n > 2. It is an open problem to find out which are the properties required for D, x to satisfy the so-called Logarithmic Comparison Theorem (LCT), ...
Artículo
Testing the Logarithmic Comparison Theorem for Free Divisors
(Taylor and Francis, 2004)
Artículo
A vanishing theorem for a class of logarithmic D-modules
(Cornell University, 2007)
Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on X = Cn. Let D X be a locally weakly quasi-homogeneous free divisor defined by ...
Artículo
Comparison of theoretical complexities of two methods for computing annihilating ideals of polynomials
(2005)
Let f1, . . . , fp be polynomials in C[x1, . . . , xn] and let D = Dn be the n-th Weyl algebra. We provide upper bounds for the complexity of computing the annihilating ideal of f s = f s1 1 · · · f sp p in D[s] = D[s1, . ...
Artículo
Explicit Comparison Theorems for D -modules
(Elsevier, 2001)
We prove in an explicit way a duality formula between two A2-modules Mlog and Mflog associated to a plane curve and we give an application of this duality to the comparison between Mflog and the A2-module of rational ...
Artículo
Quasi-free divisors and duality
(Elsevier, 2004)
We prove a duality theorem for some logarithmic D-modules associated with a class of divisors. We also give some results for the locally quasi-homogeneous case.