Effective generation for foliated surfaces: Results and applications

Abstract We explore the birational structure and invariants of a foliated surface ( X , F stretchy="false">) (X,\mathcal{F}) in terms adjoint divisor K + ϵ ⁢ K_{\mathcal{F}}+\epsilon K_{X} , 0 < ≪ 1 0<\epsilon\ll 1 . then establish bound on automorphism group an general type provide degree curve invariant by algebraically integrable foliation prove that set