Critical points and resonance of hyperplane arrangements

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.

revised version, Canadian Journal of Mathematics, to appear

References in corpus (1)

• Resonant local systems on complements of discriminantal arrangements and sl_2 representations

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