The face lattice of hyperplane arrangements

The Topology of Hyperplane Arrangements

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...

Complex Hyperplane Arrangements

We were fortunate to spend the 2004 fall semester in residence at MSRI, participating in the program on Hyperplane Arrangements and Applications. It was an intense, stimulating, productive, enlightening, eventful and most enjoyable experience. It was especially so for us long-timers in the field because the program truly marked a coming-of-age in the evolution of the subject from relative obscu...

Projection Volumes of Hyperplane Arrangements

We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones are given by the coefficients of the characteristic polynomial of the arrangement. This settles the conjecture of Drton and Klivans that this held for all finite real reflection arrangements. The methods used are geometric and combinatorial. As a consequence we determine that the angle s...

Jumping Numbers of Hyperplane Arrangements

M. Saito [S] proved that the jumping numbers of a hyperplane arrangement depend only on the combinatorics of the arrangement. However, a formula in terms of the combinatorial data was still missing. In this note, we give a formula and a different proof of the fact that the jumping numbers of a hyperplane arrangement depend only on the combinatorics. We also give a combinatorial formula for part...