In this note we determine the Bernstein-Sato polynomial bQ(s) of a generic central arrangement Q = ∏k i=1 Hi of hyperplanes. We establish a connection between the roots of bQ(s) and the degrees of… (More)

In this paper we present algorithms that compute certain local cohomology modules associated to a ring of polynomials containing the rational numbers. In particular we are able to compute the local… (More)

Let X = C n. In this paper we present an algorithm that computes the cup product structure for the de Rham cohomology ring H dR (U; C) where U is the complement of an arbitrary Zariski-closed set Y… (More)

We collect some information about the invariants λp,i(A) of a commutative local ringA containing a field introduced by G. Lyubeznik in 1993 (Finiteness properties of local cohomology modules, Invent.… (More)

We study a question raised by Eisenbud, Mustaţǎ, and Stillman regarding the injectivity of natural maps from Ext modules to local cohomology modules. We obtain some positive answers to this question… (More)

We study A-hypergeometric systems H A (β) in the sense of Gelfand, Kapranov and Zelevinsky under two aspects: the structure of their holonomi-cally dual system, and reducibility of their rank module.… (More)

The Euler–Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler–Koszul homology with D-module direct images from the… (More)

A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control.… (More)

We analyze the behavior of the holonomic rank in families of holonomic systems over complex algebraic varieties by providing homological criteria for rank-jumps in this general setting. Then we… (More)

Let X = C. In this paper we present an algorithm that computes the de Rham cohomology groups H dR(U, C) where U is the complement of an arbitrary Zariski-closed set Y in X . Our algorithm is a merger… (More)