Effective generation for foliated surfaces: Results and applications

We explore the birational structure and invariants of a foliated surface ( X , F ) in terms of the adjoint divisor K-F + epsilon K-X, 0 < epsilon & laquo; 1 0 . We then establish a bound on the automorphism group of an adjoint general type foliated surface ( X , F ), provide a bound on the degree of a general curve invariant by an algebraically integrable foliation on a surface and prove that the set of ??-adjoint canonical models of foliations of general type and with fixed volume form a bounded family.