Critical points and resonance of hyperplane arrangements
Algebraic Geometry
2019-08-15 v2 Combinatorics
Abstract
If F is a master function corresponding to a hyperplane arrangement A and a collection of weights y, we investigate the relationship between the critical set of F, the variety defined by the vanishing of the one-form w = d log F, and the resonance of y. For arrangements satisfying certain conditions, we show that if y is resonant in dimension p, then the critical set of F has codimension at most p. These include all free arrangements and all rank 3 arrangements.
Keywords
Cite
@article{arxiv.0907.0896,
title = {Critical points and resonance of hyperplane arrangements},
author = {D. Cohen and G. Denham and M. Falk and A. Varchenko},
journal= {arXiv preprint arXiv:0907.0896},
year = {2019}
}
Comments
revised version, Canadian Journal of Mathematics, to appear