Construction of minimal and canonical models for adjoint foliated structures aK_F + (1-a)K_X + D on smooth projective surfaces, within the minimal model program for foliations. The result gives effective control of the pluri-adjoint linear systems |m(K_F + D)| -- bounding the multiple m at which the system becomes basepoint-free and defines the canonical model -- and thereby yields an effective answer to the Hacon-Langer boundedness problem for adjoint foliated surfaces of general type, via Zariski decomposition of the pseudo-effective adjoint class and contraction of the negative part.
For an adjoint foliated structure on a smooth projective surface -- a foliation F paired with a boundary divisor D and a coefficient so that the relevant adjoint canonical class takes the form aK_F +…