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A central question in arrangement theory is to determine whether the characteristic polynomial    Δ  q    of the algebraic monodromy acting on the homology groupH  q    (  F   (  A  )   ,  C  )of the Milnor fiber of a complex hyperplane arrangement   A   is determined by the intersection lattice    L  (  A  )   . Under simple combinatorial conditions, we show that the multiplicities of the factors of    Δ  1    corresponding to certain eigenvalues of order a power of a prime   p   are equal to the Aomoto–Betti numbersβ  p    (  A  )    , which in turn are extracted from    L  (  A  )   . When   A   defines an arrangement of projective lines with only double and triple points, this leads to a combinatorial formula for the algebraic monodromy. To obtain these results, we relate nets on the underlying matroid of   A   to resonance varieties in positive characteristic. Using modular invariants of nets, we find a new realizability obstruction (over   C  ) for matroids, and estimate the number of essential components in the first complex resonance variety of   A  . Our approach also reveals a rather unexpected connection of modular resonance with the geometry ofSL  2    (  C  )    ‐representation varieties, which are governed by the Maurer–Cartan equation.

The Milnor fibration of a hyperplane arrangement: from modular resonance to algebraic monodromy