Skein modules and character varieties of Seifert manifolds

We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold M is finitely generated over ZA^ 1 if and only if M is irreducible and non-Haken. We analyze in detail the character varieties X (M) of such manifolds and show that under mild conditions they are reduced. We compute the Kauffman bracket skein modules for these 3-manifolds (over Q (A) ) and show that their dimensions coincide with |X (M) |.