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Artículo
Gevrey solutions of irregular hypergeometric systems in two variables
(Elsevier, 2011-08-01)
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with ...
Artículo
Gevrey expansions of hypergeometric integrals I
(Oxford University Press, 2015)
We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we consider the case of the systems associated with a one row matrix, for which the integration domains ...
Artículo
Cohomology of the complement of a free divisor
(American Mathematical Society, 1996-08)
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 ...
Artículo
Irregular modified A-Hypergeometric systems
(American Mathematical Society, 2015)
A modified A-hypergeometric system is a system of differential equations for the function f(t w · x) where f(y) is a solution of an A-hypergeometric system in n variables and w is an n dimensional integer vector, which is ...
Artículo
Localization at hyperplane arrangements: combinatorics and D-modules
(Elsevier, 2007-10-15)
We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is ...
Artículo
Computing localizations iteratively
(Cornell University, 2011)
Let R = C[x] be a polynomial ring with complex coefficients and DX = Chx, ∂i be the Weyl algebra. Describing the localization Rf = R[f −1 ] for nonzero f ∈ R as a DX-module amounts to computing the annihilator A = ...
Artículo
An algebraic approach to Integer Portfolio problems
(2011-05-01)
Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model. We propose an algebraic approach to ...
Artículo
Explicit calculations in rings of differential operators
(Société Mathématique de France, 2004)
We use the notion of a standard basis to study algebras of linear differential operators and finite type modules over these algebras. We consider the polynomial and the holomorphic cases as well as the formal case. Our ...
Artículo
The Gröbner fan of an An-module
(Elsevier, 2000-06-14)
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 ...
Artículo
On irregular binomial D-modules
(Springer, 2012-12)
We prove that a holonomic binomial D–module MA(I, β) is regular if and only if certain associated primes of I determined by the parameter vector β ∈ Cd are homogeneous. We further describe the slopes of MA(I, β) along a ...