Vadim Schechtman, Hiroaki Terao, Alexander Varchenko

1994

In this paper we strenghten a theorem by Esnault-Schechtman-Viehweg, [3], which states that one can compute the cohomology of a complement of hyperplanes in a complex affine space with coefficientsâ€¦ (More)

Yuzvinsky [7] has shown that free arrangements are formal. In this note we define a more general class of arrangements which we call k-formal, and we show that free arrangements are k-formal. Weâ€¦ (More)

Let V be an l-dimensional Euclidean space. Let G âŠ‚ O(V ) be a finite irreducible orthogonal reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomialâ€¦ (More)

Let âˆ† be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra C(âˆ†) of rational functions generated by {1/Î± | Î± âˆˆ âˆ†}.â€¦ (More)

Let q be a positive integer. In [8], we proved that the cardinality of the complement of an integral arrangement, after the modulo q reduction, is a quasi-polynomial of q, which we call theâ€¦ (More)

We consider a moduli space of combinatorially equivalent family of arrangements of hyperplanes (e.g., n distinct points in the complex line). A compactification of the moduli space is obtained byâ€¦ (More)

Given a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial. Using thisâ€¦ (More)

Let V be Euclidean space. Let W âŠ‚ GL(V ) be a finite irreducible reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H âˆˆ A chooseâ€¦ (More)

Let W be a nite group generated by unitary re ections and A be the set of re ecting hyperplanes. We will give a characterization of the logarithmic di erential forms with poles along A in terms ofâ€¦ (More)

Let âˆ† be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra R(âˆ†) of rational functions on V which are regularâ€¦ (More)