  Let A=k+A_1+A_2.... be a connected graded, noetherian k-algebra that is
generated in degree one over an algebraically closed field k. Suppose that the
graded quotient ring Q(A) has the form Q(A)=k(Y)[t,t^{-1},sigma], where sigma
is an automorphism of the integral projective surface Y. Then we prove that A
can be written as a naive blowup algebra of a projective surface X birational
to Y. This enables one to obtain a deep understanding of the structure of these
algebras; for example, generically they are not strongly noetherian and their
point modules are not parametrized by a projective scheme. This is despite the
fact that the simple objects in the quotient category qgr A will always be in
(1-1) correspondence with the closed points of the scheme X.
