Motivic cohomology of the complement of 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 ...

The Topology of Hyperplane Arrangements

An Overview of Motivic Cohomology

In this talk we give an overview of some of the motivations behind and applications of motivic cohomology.We first present aK-theoretic timeline converging onmotivic cohomology, then briefly discuss algebraic K-theory and its more concrete cousin Milnor K-theory. We then present a geometric definition of motivic cohomology via Bloch’s higher Chow groups and outline the main features of motivic ...

Hodge Spectrum of Hyperplane Arrangements

In this article there are two main results. The first result gives a formula, in terms of a log resolution, for the graded pieces of the Hodge filtration on the cohomology of a unitary local system of rank one on the complement of an arbitrary divisor in a smooth projective complex variety. The second result is an application of the first. We give a combinatorial formula for the spectrum of a h...

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