SAKAI'S THEOREM FOR Q-DIVISORS ON SURFACES AND APPLICATIONS

摘要

In this paper, we present a characterization of a big Q-divisor D on a smooth projective surface S with D-2 0 and (Os(-[D])) not equal 0, which which generalizes a result of Sakai [Sak90] for D integral. As applications of this result for [Ks + [d]].These results can be viewed as refinements of previous results on smooth surfaces of Fin-Lazarsfeld [EL93] and Masek [mas99].