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arXiv · 0907.0896

Critical points and resonance of hyperplane arrangements

D. Cohen·G. Denham·M. Falk·A. Varchenko
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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.

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D. Cohen, G. Denham, M. Falk, A. Varchenko. 2009-07-05. Critical points and resonance of hyperplane arrangements. https://doi.org/10.4153/cjm-2011-028-8

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