ALMOST KÄ HLER FORMS ON RATIONAL 4-MANIFOLDS.

We study Nakai-Moishezon type question and Donaldson's "tamed to compatible" question for almost complex structures on rational four manifolds. By extending Taubes' subvarieties-current-form technique to J-nef genus 0 classes, we give affirmative answers of these two questions for all tamed almost complex structures on S2 bundles over S2 as well as for many geometrically interesting tamed almost complex structures on other rational four manifolds, including the del Pezzo ones. [ABSTRACT FROM AUTHOR]