Critical Points and Resonance of Hyperplane Arrangements
Printed: Oct 2011
If Φλ is a master function corresponding to a hyperplane arrangement
A and a collection of weights λ, we investigate the relationship
between the critical set of Φλ, the variety defined by the vanishing
of the one-form ωλ = d logΦλ, and the resonance of λ.
For arrangements satisfying certain conditions, we show that if λ is
resonant in dimension p, then the critical set
of Φλ has codimension
at most p. These include all free arrangements and all rank 3 arrangements.
hyperplane arrangement, master function, resonant weights, critical set
32S22 - Relations with arrangements of hyperplanes [See also 52C35]
55N25 - Homology with local coefficients, equivariant cohomology
52C35 - Arrangements of points, flats, hyperplanes [See also 32S22]