BOUNDEDNESS OF LOG-PLURICANONICAL MAPS FOR SURFACES OF LOG-GENERAL TYPE IN POSITIVE CHARACTERISTIC

In this article we prove the following boundedness result: Fix a DCC set I ⊆ [0, 1]. Let D be the set of all log pairs (X, Δ) satisfying the following properties: (i) X is a projective surface defined over an algebraically closed field, (ii) (X, Δ) is log canonical and the coefficients of Δ are in I, and (iii) Kₓ + Δ is big. Then there is a positive integer N = N(I) depending only on the set I such that the linear system |⎿m(Kₓ +Δ)⏌| defines a birational map onto its image for all m ≥ N and (X, Δ) ∈ D