Critical points and resonance of hyperplane arrangements

Details Critical points and resonance of hyperplane arrangements Critical points and resonance of hyperplane arrangements

2009-07-05

arxiv.org/abs/0907.0896v2

Mathematics

Algebraic Geometry

revised version, Canadian Journal of Mathematics, to appear

Scientific paper

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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