Effective Matsusaka's Theorem for surfaces in characteristic p

We obtain an effective version of Matsusaka's theorem for arbitrary smooth algebraic surfaces in positive characteristic, which provides an effective bound on the multiple which makes an ample line bundle D very ample. The proof for pathological surfaces is based on a Reider-type theorem. As a consequence, a Kawamata-Viehweg-type vanishing theorem is proved for arbitrary smooth algebraic surfaces in positive characteristic.