On Yuzvinsky’s lattice sheaf cohomology for hyperplane arrangements

Hyperplane arrangements, M-tame polynomials and twisted cohomology

Let A = {H1, ..., Hd} be an affine essential hyperplane arrangement in C , see [OT1], [OT2] for general facts on arrangements. We set as usual M = M(A) = C\X, X being the union of all the hyperplanes in A. One of the main problems now in hyperplane arrangement theory is to study the cohomology of the complement M with coefficients in some local system L on M , see for instance the introduction ...

On a Vanishing Result in Sheaf Cohomology

The goal of this note is to give an example for which Theorem 1.1 fails if we only relax the hypothesis that X is quasi-compact (Propositions 2.3 and 3.1). This example emerged from the author’s investigation on local cohomology of valuation rings [Dat16]. In particular, some results from [Dat16, Sections 6, 7] are reproduced below without citation. Any other outside result we use is accompanie...

Generalised sheaf cohomology theories

This paper is an expanded version of notes for a set of lectures given at the Isaac Newton Institute for Mathematical Sciences during a NATO ASI Workshop entitled “Homotopy Theory of Geometric Categories” on September 23 and 24, 2002. This workshop was part of a program entitled New Contexts in Stable Homotopy Theory that was held at the Institute during the fall of 2002. The intent for the lec...

Cohomology Bases for the De Concini -procesi Models of Hyperplane Arrangements and Sums over Trees

On Zones of Flats in Hyperplane Arrangements

Let H be a set of n hyperplanes in R d , let A(H) be its arrangement, and let b be an m-dimensional at. The zone of b in the arrangement A(H) is the set of open d-dimensional cells of A(H) which are intersected by b. We prove that the maximum number of incidences of k-cofaces of the arrangement with cells of the zone is O(n minfk+m;b d+m 2 cg k;d;m (n)), where k;d;m (n) = log n ifm 1, d+m is od...