  We study the irreducibility of resonance varieties of graded rings over an
exterior algebra E with particular attention to Orlik-Solomon algebras. We
prove that for a stable monomial ideal in E the first resonance variety is
irreducible. If J is an Orlik- Solomon ideal of an essential central hyperplane
arrangement, then we show that its first resonance variety is irreducible if
and only if the subideal of J generated by all degree 2 elements has a 2-linear
resolution. As an application we characterize those hyperplane arrangements of
rank less than or equal to 3 where J is componentwise linear. Higher resonance
varieties are also considered. We prove results supporting a conjecture of
Schenck-Suciu relating the Betti numbers of the linear strand of J and its
first resonance variety. A counter example is constructed that this conjecture
is not true for arbitrary graded ideals.
