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We give a vanishing theorem for the monodromy eigenspaces of the Milnorfibers of complex line arrangements. By applying the modular bound of the localsystem cohomology groups given by Papadima-Suciu, the result is deduced fromthe vanishing of the cohomology of certain Aomoto complex over finite fields.In order to prove this, we introduce degeneration homomorphisms ofOrlik-Solomon algebras.

Degeneration of Orlik-Solomon algebras and Milnor fibers of complex line arrangements